I'm sure /u/qhapaqocha is going to come in and hit this out of the park, but I'll make a first pass at it, if that's alright. I can think of four ways women could attain positions of high rank within the Inca system of government.
The first and probably most obvious is to marry the Emperor, the Sapa Inca. His official wife —who was almost always one of his sisters or half-sisters (not step-sisters, thank you to u/MooseFlyer for catching my mistake)— held the position of Coya, Empress, which came with a good deal of religious veneration in addition to the soft power that comes from having ready access to the most powerful man in the Inca world. Below the Coya there were other wives and concubines —both related and unrelated to the emperor— and they had as much personal power and authority as their personal relationship to the emperor and their status as mother of various princes and princesses determined. Imperial favourites and mothers to prominent royals were women of great influence.
The second position that immediately comes to mind is to be the head of a Panaca. The Panaca is an institution unique to the Inca. Emperors were mummified upon their death, and that mummy continued to hold a court in its palace, ruling over much of its former estate, forever. The trouble with a mummified emperor, of course, is that it doesn't talk much. How do you know what it wants to do with all that wealth? Well, a cult of royal courtiers formed around the mummy and interpreted its wishes. Any Inca could join a Panaca —although only one Panaca, and their powers and influences did vary— and this became an avenue for both men and women of unimportant birth or low reputation to align themselves with an organization whose power might almost rival that of the current Sapa Inca. The inner circle around a mummy was often almost entirely female, and though we do not know quite how leadership within the Panaca's courtiers was decided, it may well be that the fact that men had other career opportunities outside the cult dedicated to a mummified emperor saw ambitious women commit themselves more fully to climbing up through the ranks to wield real power over the wealth of the deceased emperors.
Third, Chosen Women were beautiful girls taken from their parents by the Inca State and put into special houses until they were married to either the Emperor, one of the Emperor's favourites, or to Inti, the Sun God who was the patron god of the Inca.* Now a Chosen Woman had little power, it is true, but a Bride of the Sun who went on to become the leader of a House of Chosen Women —especially the large ones in Cuzco and on the Island of the Sun in Lake Titicaca (then Lake Chucuito)— might be equated to a Mother Superior or an Abbess of a particularly powerful religious institution. What happened within the walls of her domain were her business, and her House of Chosen Women had enormous influence on what happened in the surrounding area.
Finally, the Inca were polytheists, and they were very open to the gods and cults of the people they absorbed into their empire, provided the superiority of the Inca pantheon was acknowledged. In that spirit, female religious leaders and especially women with oracular powers were given as much power within Tahuantinsuyu as they would have held before their worshipers were amalgamated into the Empire. The Inca were also willing to creating new female religious figures of enormous power. Probably the best example of this happened when Mama Ocllo —Coya to Topa Cusi Yupanki and mother of Huanya Capac— died. Huayna Capac adored his mother, and so he commissioned the creation of a new state cult in her honour, including a young woman to be known as Mama Ocllo's Voice, who had the ability to speak on his mother's behalf. Years later during the great revolt when the northern third of the Empire (roughly Ecuador) revolted, several units of pure-blooded Inca were embarrassed during a siege and then publicly berated by Huayna Capac. Now the rest of the Inca military were soldiers fulfilling their tax labour quota, but pure-blooded Inca —Pacuyoks, Ear-Plug Men— considered themselves to be volunteers. They decided to 'unvolunteer' and march home to Cuzco, and only the timely intervention of Mama Ocllo's Voice heaping them with praise and promising them riches turned the deserters around.
To circle back to your reference to Yzma, while none of these are a perfect fit for her, I think from context we can establish she's not married to the Emperor, and if she was running a Panaca we would see her in close proximity to a mummy and speaking on its behalf. If she was a Bride of Inti running a House of Chosen Women, she wouldn't have Kronk as a henchman, because Houses of Chosen Women were exclusively female domains. Yzma —to the extent that Disney cares about such things— almost certainly was some kind of witch or religious figure. She clearly has magical abilities and the freedom and power to go where she wants, when she wants, doing what she wants.
As a footnote, let me explain that asterisk I put after Inti the sun god who was the patron of the Inca. There is a lot we don't know about the Inca religion. There is a theory that I like the sound of that suggests Inti was not actually the Imperial patron in the Inca pantheon. He was more the patron god of their empire-building. As Tahuantinsuyu grew, the Inca built sun temples on heights overlooking their conquered peoples to let the new citizens know who was boss, but Inti as an Empire Builder and Huanacauri as their war idol were probably much more cults of conquest than of true reverence to the Inca. Viracocha, the Creator God and head of the Inca pantheon, was probably the true patron of the Inca, but they did not create many new temples to honour him during the course of their empire-building. They did maintain and glorify the places where others worshiped him, though.
Edit: Minor edits for clarity.
Edit 2: Half-sisters, not step-sisters.
This is an excellent question, and I'm going to complicate it by asking, "what do you mean by power?" The Inca had a complex interweaving of social, sacred, economic, and political power, and the history of the Andes had examples of women attaining power of various stripes long before the Inca. To give two brief examples predating the Inca:
Archaeological excavations in coastal Ecuador at the site of Capa Perro recovered the burial of a shaman, or perhaps an initiate, of a young woman, some 14-18 years old. She was interred with numerous accoutrement depicting her role in society: a coquero (perhaps antique for her having been passed down), which is a small lime pot used to activate coca leaves' alkaloids while chewing; greenstone pendants (green being a collor of fertility and preciousness throughout the Americas) and a fruit bat mandible found in the abdominal region; and a fragmented ceramic figurine that was found in the disarticulated remains of a feline snout. More recent work in Bolivia has recovered a fox-snout pouch with residues of hallucinogenic drugs, and it's possible we are looking at another example of one of these Andean "bags of holding" for shamanic paraphernalia. This young woman dated from Terminal Valdivia times, some 1800-1500 BC - so at this early time within Andean social complexity, some societies held women as authorities in religious matters.
Let's turn the clock forward a bit more to the Moche of the north Peruvian coast. There, at the site of El Brujo, Peruvian archaeologists recovered a female mummy now known as the "Lady of Cao". As you can see from the picture link I just attached, the lady of Cao was interred with a remarkable array of gold, including a sizable hammered-gold headdress and two massive golden war clubs (ceremonial). The Lady of Cao has been posited as a ruler or dynast of El Brujo, itself a sizable Moche settlement - so in the early centuries AD among the Moche there is evidence of women within the ruling class not only in a religious sense, but politically, with implications for military strategy and legitimacy.
With some of this historical background in mind, let's look at the Inca. The position of Sapa Inca, in the chronicles and dynastic lists compiled, were always men. However, their queen, the Qoya, was also imbued with immense power. Being of Inca stock herself (by blood - think Targaryens or Habsburgs, so sisters or first cousins), the Qoya provided counsel to her husband and acted as a chief political advisor and ally for the emperor's policies. Being the primary Qoya carried immense weight, as queen or queen mother. However, the Sapa Inca married secondary wives as well, often to cement political alliances with ethnic groups to be brought into the imperial fold. Wayna Qhapaq had something like a dozen wives, and some fifty children, which is what precipitated the fraternal civil war of the 1520s, when he and his chosen heir Ninan Kuychi died unexpectedly. The Qoya, being part of the Inca extended royal family, held especially great power in determining how these heirs were selected; this is because a Sapa Inca, rather than strictly taking his father's name and kin group, founded his own kin group or panaqa (some have called these royal corporations, or dynastic lineages). Each new panaqa, while claiming legitimacy from their father going back to Manqo Qhapaq (the mytho-historical first Inca), seated their power in practice to the ruler's mother. This meant they were often the primary advocates for their sons' political fortunes, and commanded immense wealth which they had full autonomy to distribute. (Unfortunately, much of this courtroom intrigue has been lost to history.) As in the cases of Inca mummies of the Sapa Inca, the Qoya's mummy and image also maintained this power after death. However, this heightened power also meant higher stakes - Wayna Qhapaq, upon taking the throne in the typical coup of legitimacy, banished the failed heir to the throne but executed his mother.
This is all in addition to the institution of the aqllakuna, the Chosen Women commonly referred to in surveys of the Inca. These high-status retainers selected by the Inca, and secluded in acllawasi, were essentially given a cotillion of sorts, with training in textile production, political and military strategy, religion, and history; their destiny was that of being consorts to the Inca elite (or their mummies), or else being tactfully deployed wives for marriage to potential allies and subjects. As you might expect, however, our knowledge of women in Inca society, as elsewhere in history, is limited when compared to men, and often colored through male gazes and voices.
EDIT: Whoops, sources:
D'Altroy's Incas has a good section on the queen for more information, that's what I consulted for this.
Zeidler, James A., Peter W. Stahl, and Marie J. Sutliff 1998 Shamanistic Elements in a Terminal Valdivia Burial, Northern Manabí, Ecuador. In Recent Advances in the Archaeology of the Northern Andes: In Memory of Gerardo Reichel-Dolmatoff, edited by Augusto Oyuela-Caycedo and J. Scott Raymond, pp. 109–120. Cotsen Institute of Archaeology, UCLA, Los Angeles.
Ziolkowski, Mariusz 1996 La guerra de los wawqi: los objetivos y los mecanismos de la rivalidid dentro de la elite Inka, siglos XV-XVI. Ediciones Abya-Yala, Quito.
My main focus isn't on women in America's, but I have overlapped into that area before. I had to do a quick google search to remind myself what Yzma did in the movie, but it sounds like she was an advisor to the emperor and eventually wanted to kill him to take his spot.
In that way, Yzma would not have been able to obtain the throne and become a ruler, but she certainly could have been in a significant political position in Incan society. While it may have not been in an advisory role in the sense of how we view advisors to leaders today, women in Incan/Andean society were still able to obtain significant social/political power.
Historian Karen Powers defines the Pre-Colombian Incan society as "gender parallelism." Powers writes that "Before the Spanish arrival, the peoples of the Andes put together societies that were characterized by gender parallelism and gender complementarity. In gender-parallel societies, women and men operate in two separate, but equivalent spheres, each gender enjoying autonomy in its own sphere. For example, in Inca society, women had their own religious and political organizations with their own female hierarchies of priestesses and officials, as did men in their sphere. Although men and women functioned in separate, gender-specific spheres, their worlds were highly interdependent and were joined together at the apex of the political system through the rule of a paramount lord and his council."
This separation of gender was not created to be unfair or to restrict women, however, as they were often viewed as existing next to each other and working with each other in social and political goals. Women were able to pass property down to their daughters the same way fathers were able to pass goods down to their sons. This is in contrast to how the Spanish would upend society in the coming centuries when they arrived. Women were able to obtain the role of Curacas that were able to make significant choices in local matters dealing with access to material and goods produced by the community.
Above the community level and more at the 'national' level that Yzma would have been, women had considerable influence. Again, Powers writes, "Power often came to men through women. It should also be noted that at earlier stages of Andean political formation, some women had exercised power as paramount rulers." While women were still seperated by gender parallelism, women could still impact political outcomes by voting and/or advising. While advising may seem like a weak term, these women were also held in esteem and respected, thus were able to hold influence. This did not mean that women were equal in all regards, however, given that ultimate political power still resided in the male heirarchy. While women with political influence like Yzma may have existed within the religious/political structure of Incan/Andean cultures, Yzma would not have been able to cross over from the female political/religious sphere and become the absolute ruler of the Incan empire.
sources:
Silverblatt, Irene. "Andean Women in the Inca Empire." Feminist Studies 4, no. 3 (1978): 37-61. Accessed May 15, 2020. doi:10.2307/3177537.
Powers, Karen Vieira. "Andeans and Spaniards in the Contact Zone: A Gendered Collision." The American Indian Quarterly 24, no. 4 (2000): 511-536. doi:10.1353/aiq.2000.0025.
Anton, Ferdinand, and Marianne Herzfeld. 1973. Woman in pre-Columbian America.
edit- looks like /u/qhapaqocha is the subject matter expert! She has an awesome write up more articulately stated!
