Mountains don't preclude rivers or other water resources such as lakes. Both the Aztec and Inca were based in fertile lacustrine basins, Texcoco and Titicaca, respectively. Since I'm more familiar with Mesoamerica, we'll focus on that region.

Just sticking with maize agriculture, the specific origin point of domestication is still debated, but the general consensus is that it took place in the Tehuacan valley (MacNeish & Eubanks 2017). This area is set back from the Gulf Coast in a mountain valley that is relatively dry, though the paleoclimate may have been somewhat cooler. Nevertheless, the origins of agriculture do not require ideal locations for plant growth, and in fact a less optimal climate may spur development of horticulture relative to areas with more abundant wild resources.

Of course, we're not talking about the origins of agriculture, but the intensification of agriculture leading to complex, sedentary societies, i.e., the kind of settlements that lead to empires. On this topic, Mesoamerican intensive agriculture… starts near rivers (and lakes). The Grijalva river shows evidence of maize cultivation shortly after the domestication event in the Tehuacan region, more than 6000 years ago (Pope et al., 2001). The Balsas river (a contender for the site of maize domestication) was another early site of maize agriculture, and it's tributary, the Atoyac flows right through the Valley of Oaxaca (Rojas & Beccan Davila 2019). The Soconusco region, along the Pacific coast where modern day Mexico and Guatemala meet, is streaked with small rivers flowing down from the Sierra Madres. The Suchiate river, for example, runs right by the important early site of Izapa. On the other coast, the Coatzcacalcos river basin gave rise to the earliest Olmec settlements, including San Lorenzo.

Arnold (2009) points out that it was not so much strict reliance on a river that facilitated growth in the Olmec heartland, but exploitation of wetland environments, including periodic flooding. The ebb and flow of water into marshy areas acted like a natural system of irrigation for maize agriculture in an environment that the proto-Olmec were already exploiting for other plant resources as well as an array of fish and game. Similar use of periodic wetlands has been posited as a major factor in early Maya lowland cities, such as El Mirador. The use of “bajos” which turned into small lakes and marshes during the rainy season not only provided hydrologic resources to exploit, but also presaged the development of human-made reservoirs (Dunning et al., 2004).

Elsewhere, lakes provided the hydraulic impetus for settlement. The Formative Maya site of Kaminaljuyu, for instance, was built around a (now desiccated) lake and had a network of canals (Popenoe de Hatch et al., 2002). Lake Patzcuaro in Michoacan hosted many peoples prior to becoming the center of the Purepecha kingdom. Of course, the most famous lake in Mesoamerica is Lake Texcoco, in the Basin of Mexico. Really a series of lakes that contracted to separate and expanded to conjoin with the alternating dry and rainy seasons, the Basin of Mexico lake system has long hosted human settlement. The waters in the western and southern portions are "sweeter," less brackish and saline than the shallower waters to the east and north. Predictably, this is where we see very early polities. Tlatilco, a contemporary of the Olmecs, was located on the western banks, near where the Tepanecs would found Azcapotzalco many centuries later. Tlapacoya, which may have the earliest evidence of permanent human habitation in the area, was located in the southwest, near the future site of Chalco. Cuicuilco, an ancient site that was inhabited into the Classic period, was located in the southwest, uncomfortably close to the Xitle volcano.

The point of this meandering hydrological tour of Mesoamerica is to point out that the deciding factor for early sedentary agricultural centers was not mountains, but water. There is an older theory of “hydrological empires,” wherein the need to organize labor for large-scale irrigation projects acts as the impetus to establish a social hierarchy and bureaucratic state. Like so many olde timey all-encompassing social models its search for a universal truth overrode a more nuanced view of human societies as stimulated by multifactorial causes in idiosyncratic ways. However, the basic premise of agriculture being the most effective way to guarantee a large population in diverse landscapes, and specialized social roles arising from such a population, is sound. Societal complexity and specialization can, in turn, lead to more efficient exploitation of resources. For instance, in the Soconusco region early agriculture is associated with a shift away from more localized and forgeable food items to an intensification and expansion of the staple crop, maize, to areas less suited to casual horticulture. At the same time, monumental architecture starts to crop up, indicating, if not necessarily a social hierarchy, at least a social organization capable of marshaling mass labor for ideological (rather than subsistence) projects (Rosenswig et al., 2015). The Valley of Oaxaca, an area described by Flannery and Marcus (1976) as in a state of "permanent drought," saw nascent state formation around areas of relatively more stable land, but the most important site in the Valley, Monte Alban, is notably not situated to take direct advantage of these areas. Instead, the city acted as a centrally located and defensible site to exert political control over productive farmland.

Empires are, to be bracingly reductionist, assemblages of people, and people have an unfortunate habit of dying horribly when not fed and sometimes acting in extreme ways to prevent their own starvation. While early state formation may be buoyed by the presence of abundant and easily exploited resources to prevent this, control of these resources may also come via indirect means. These methods may be coercive or cooperative, utilizing political, economic, or religious power, or any mix of the above. Many nascent states did arise in areas where rapidly available foodstuffs could give rise to populations that could further refine their ability to generate even more sustenance, through everything from refinement of staple crops to proto-bureaucratic methods. Once that early state template is established, however, it can be adopted and adapted to suit the needs of people in areas perhaps not as bountiful that could nevertheless sustain a sedentary, complex, and stratified society. Sometimes the relative harshness of the land can itself act as an impetus for these changes, but the end result is a positive feedback loop of increased population leading to the need for internal systems for more efficient and expansive use of resources leading to increased population and so forth, until some internal or external factor goes array and cause the whole system to short-circuit.

This is a vastly oversimplified view of pre-modern agricultural states, but it's a helpful model to keep in mind for your question because it reinforces that wetlands friendly to growing maize (and other crops) were key to the earliest states in Mesoamerica. The mountains were incidental, because Mesoamerica, quite frankly, has a lot of mountains. Central Mesoamerica in particular is basically a series of valleys.

To close out on a bit of tangent though, the ubiquity of mountains in many parts of Mesoamerica did mean they were often imbued with spiritual significance. Among the Aztecs, rain was thought to issue from mountain caves and thus mountains were associated with Tlaloc, the rain god. Tlaloc and his minor helper deities, the tlatoque, were associated with specific mountains, and worship of this complex of rain-mountain deities manifested in Aztec households through Tepictoton, small idols modeled from amaranth. Sahagun reports these figures were stamped with images or otherwise decorated to evoke a particular god. During the month of Tepeilhuitl, these figures played a central role in creating a sort of temporary altar in Aztec homes which reflected both the spiritual and geographical topography of the world around them. Afterwards, the dough idols would be eaten, the Aztecs literally internalizing the divine forces of the cosmos (and not wasting any delicious amaranth!). Fitzgerald (2019) has a good summary of the sources for tepictoton and a discussion of their significance, if you are interested. The major point of this closing aside, however, is to close the loop on the question of “mountains vs. water,” by noting that, to Mesoamericans, there was no such dichotomy, they were part of the same ecological and spiritual complex.