Completely spitballing, it’s possible the Republic could have transitioned into the Empire gradually enough that you really can’t strictly say Year X was the Republic, Year Y was the Empire. There’s nothing textual that supports this, but it fits in with the metaphor for American Imperialism.
This firmly plants the start of the Empire at their birth. Why? Vader did not know Luke had a sister which means he was not present at the birth. So the event that turned Vader and started the Empire happened between conception and birth of the twins.
I don’t think we can necessarily assume that Vader turning to the dark side and the rise of the Empire happened at the same time.
There may not have been a moment as you lived through it, but historians would be able to pinpoint a moment when a key thing changed. Hunting down the Jedi could be that key thing.