Ok, this is a really cool process that involved multiple important figures pushing the boundaries of how much power one figure could hold. The path to emperor was paved mainly by Pompey, then Julius Caesar, and finally Augustus.

Pompey, Julius, and Crassus were three of the most powerful people in the Roman Empire. Crassus built an economic Empire, while Julius focused on gaining popular support and military might. However, It was Pompey who became the most powerful first. Pompey began stretching the rules about what one person could do, such as gaining the right to wear the robes of Jupiter on normal occasions, although he only tried this once and it didn't go over well.

Later, Julius gained his own power, and in an important display, showed the ability of one general to control Rome by crossing the Rubicon. This is a huge deal because it represented the power of Rome lying with the armies, not the Senate.

It is important to note the backlash against these figures. Rome did not take these extensions of power lightly. Pompey faced a lot of backlash against his actions, and of course Caesar was famously assassinated by Senators. However, this generation of monolithic entities made the prospect of one person gaining power more feasible to the Roman people, as well as weakening the Senate.

This leads us to Augustus, who led a multipart campaign to portray himself not just as the rightful ruler, but the logical and fated descendant of Rome. First, Augustus gave himself the powers of both the tribune of the plebians as well as the power of the consuls. He didn't actually take the positions, he just held that same power. The consuls were the two most important leaders in Rome, elected yearly to push the main agendas and command the armies, much like a US President. The drawback was that they only served for a year, and had to work with the other consul to get stuff done. By giving himself the powers of the consul, Augustus avoided all of these restrictions while still phrasing himself as an ordinary politician. Furthermore, he also took the powers of the Tribune of the plebs, who had broad veto powers. The combination basically gave Augustus unlimited political power and authority for life, but he phrased it in a way that made it seem like it was a loophole in the rules. Romans LOVED loopholes, and tended to view the world as a series of contracts. So, this meant Augustus didn't actually declare himself king, which would have gone over poorly- he took known Roman political powers, and made it acceptable. It's as if an extremely well liked President was made chief supreme court justice after they left office, while also being secretary of state. It's a massive amount of power, stated in known terms.

Furthermore, Augustus had an extremely strong and thorough propaganda system that connected him to the history of Rome and portrayed his ascension as inevitable. First, let's look at his house. Rather than make a mansion or palace, like his descendants, Augustus had a small house on the Palatine hill. He had the house of an ordinary senator. Furthermore, the Palestine was home to many of the oldest temples in Rome. Taking stock: there was the hut of Romulus and Remus, founders of Rome; a temple to the Magna Mater, protector of Aeneas and Rome, as well as a temple to Victory. It is no small surprise that Augustus paid to restore and remodel these temples, with an eye to emphasizing their venerability. Augustus also encouraged a particular view of Roman history focused on singular figures. The most important was Aeneas, and Augustus encouraged this myth with Virgil's Aenied. Augustus basically coerced poets to write a version of Roman history where progress was made by single men, in a famous passage where the hundred sons of Rome are traced by the Magna Mater from aeneas

The thing to remember is that it didn't happen in a vacuum. By the time of Augustus, the Roman state had been flipping in and out of civil wars and civil unrest for decades. Sulla had marched on Rome when he didn't like a law of the assembly and his men murdered the tribune responsible for it. Marius then started murdering Sullan supporters. Sulla returned and returned the favour except he made his murders legal. Sulla also took away the political rights of many opponents, denying them the right to ever hold political office.

So as you enter the age of the first triumvirate you had a subculture of very angry people who'd been denied political rights combined with some Italian peoples who'd suffered under the Social War. With the triumvirate you get a lot of civil unrest with political gangs fighting it out in the streets between the triumvirate faction and the Catonian factions. The senate is actually burned down by the supporters of one of the murdered gang leaders. That's how bad things get before the civil war between Caesar and Pompeius.

Then you had the second civil war followed by a brief respite of peace under the dictatorship of Caesar. This was short-lived and then followed by fighting between the Caesarean-faction (under Antonius) and the Republicans and then the assassins of Caesar. With that third civil war finished (alongside more political murders) you get cold war between Octavianus and Antonius which finally breaks out into another civil war leaving Octavianus the sole victor.

So this has been literally decades of unrest with many periods of open warfare raging across Italy. Rome had been repeatedly blockaded by the sons of Pompeius hampering food importation which only added to people's difficulties.

So now comes Octavianus who offers the first real peace in ages. His auctoritas was unparalleled at this time and anyone else who had similar authority had been killed off in the civil wars.

He starts by taking over the tribunician power - this is an existing Republican institution so he's not creating new powers. It makes him now the defender of the plebs and also removes the office from being used by ambitious upstarts to gain popularity. It also means no one can use the veto power against any of his legislation and he can also veto legislation that he doesn't support - well in theory, his authority at this point is so great that just his disapproval would be enough to scuttle any proposal.

He then is made proconsul for several provinces and the right to command them while staying in Rome. Again this is not new - Prompeius had done the same when he was governor of Spain. This provides two benefits, first being a proconsul he now has imperium (the legal right to command troops) but also the ability to personally appoint legates to command those troops in his provinces, people he know he can trust. These won't be ambitious senators who might eye those troops for another march on Rome, they'll often be equestrians who lack the auctoritas to make such a bid. Furthermore he graciously offers to take the provinces which are the most dangerous: Gaul, Syria, Spain, northern Greece. Since these are the provinces where the most dangers to Rome are, that's where the bulk of the legions are. So he's quickly put the majority of the armies under his personal command without making it look like a blatant power grab.

Obviously he also got elected to the consulship multiple times, but eventually he began to avoid it - he understood the murder of Caesar all too well and didn't want to hog the glory. Besides, he already had enough power and influence that he didn't need the office to get things done.

Lastly in 27 BCE he was granted the title of 'Augustus' by the senate. It's an important title because it had religious connotations. This added to that almost divine nature of his rule.

The long and short end of it is that Augustus' rule came about following decades of civil unrest and he offered peace. Anyone who could have possibly challenged him had died in the civil wars. His powers all had Republican precedents and in combination gave him, in effect, supreme power. His auctoritas was so ridiculously high that none of the surviving senators would be able to challenge him. He purposely avoided the office of dictator that would have been an easier path to sole-rule because he learned from Caesar's downfall.

Lastly it is important to remember this hatred of the kings comes to us from texts written by elites. The Republic was built to be an oligarchy with the electoral systems heavily biased towards wealth. Political conservatism ensured that the majority of consuls came from a small handful of elite families (patrician and plebeian). The lack of primary sources written by the hoi polloi makes it impossible to know if they also shared this hatred towards kings and tyrants, or if they just rolled their eyes and muttered something about 'new boss same as the old boss'.