There was not as big a jump from Dictator Caesar to Imperator Augustus as is implied in your question.

Caesar was murdered by Brutus and Cassius. The people were upset to an extent, and therefore looked to them to lead them. Even Cicero writes that they were a sinking ship. They had no plan, no money, and no men to run Rome. What do you do when your one ruler, who just abolished the typical rules of Rome, has just been assassinated, and the conspirators have no plan?

So the Senate groomed Octavian, Caesar's heir/nephew. Again, Cicero writes that they "raised, praised, and erased" Octavian, or at least intended to until he found out. Also, at this time, Mark Antony was Caesar's right hand man so he had seized power in Rome, spending all of Octavian's inheritance money on whores. Octavian hated Antony, but also needed to join up with him to kill Brutus and Cassius. (Mark Antony, Octavian and Lepidus also formed the Second Triumvirate, giving them exceptional power.)

After the decisive battle, the Senate forgot one key problem. - they'd just given a teenage boy, Caesar's declared heir no less, an army. And what did Octavian do with that army? Keep it illegally, and march on Rome. This was strictly prohibited, as it was a sign of conquering or invasion. He took the treasury and started attacks on Mark Antony, and then Cleopatra and their children. He also killed Caesar and Cleopatra's son, Caesarion, as when he grew up, he would be the legitimate heir.

So goes on of Octavian's battle of Actium against Mark Antony, and once he returns to Rome, he legitimises his adoption, and shuffles money and land to settle veterans and get his inheritance back to do work on Rome.

It was hard for Octavian at the start, as people hated him and the unjustly things he had done in his past. He was still only a teenager at this point, but he made reforms to Rome and its infrastructure, built new temples and buildings and finished building Caesar's Forum, as well as building his own. They worked in his favour, and he was gifted the title Augustus and other titles in the 1st and 2nd Settlement around 27BC -. The title Emperor didnt exist - it was known as Imperator, which, in a way, equates to a similar notion. There were still Consuls and such during Augustus' reign, but he had reformed the senate and made ages younger for roles, etc.

The proper ruling of 'Emperors' only really started after him. He started the pathway to the future one man rule, which Rome was founded on not having, due to Julius Caesar.

Also, you have to think - by the time Augustus was properly in power, a lot of the senate was dead or old, and by the time of Augustus' death, the new populous and generation would have seen his one man rule as normal.

I hope this helps in some way?

TL;DR - Senate made mistake of giving Caesar's heir an army. Heir marches on Rome, fights Mark Antony, takes over. Most old senators from then would have died during his reign so wouldn't have necessarily stopped him.