As the title says, when do you form your empires? I've only done so twice yet, both times as Rome.
The first time I did t rightaway when first offered, certainly before turn 100.
The second time is my current game where I waited a while till after I had most of what would be modern day Italy plus parts of Greece under control. That second time I also roleplayed t a bit, my republic was lead by an excellent party (good administrator plus a military trait), it was aerage in power but suddenly overthrown by a really bad party, worse, I conquered an objective that turn just after the change of government so the new one was likely to last a long time now. So I decided my victorious consul would profit from his triumph and ceize power, he couldn't be worse. Turned out he made a good emperor.
So what are the advantages of empire over republic. You reduce government age, which would be more advantageous later in the game. You produce legacy from government, that would be handy even early on. Not sure which way loyalty swings as I went from a government with a ice loyalty boost to one with bad loyalty to an empire without specific boost within three turns so a lot changed in that time, but after that move certain regions seemed to have dropped significantly in loyalty and assigning citizens to culture didn't help so more expensive loyalty buildings were needed (sometimes later a region would get a big loyalty boost for no reason I'd understand (nope, not slave trading). With the initial change from republic to empire decadence seems to drop quite a bit, but after that you have to increasingly place citizens on culture (which no longer makes a big difference for loyalty) to stay on top of the CDR and move towards a golden age. There really are so many factors that can affect all those stats that it's hard to be sure whether it's better to form an empire early or not, oh and I didn't even cover falling behind on ageing tokens once you are an empire and thereby risking massive decline.
And of course I was also constantly expanding and mentally preparing for conflict with the Antigonids who were happily gobbling up crumbling Macedonia and Ptolomeic Egypt in an everlasting civil war. Around turn 150 they are producing some 280 legacy a turn to my 150. Right now I'm trying to settle matters once and for all with Carthage (seize all provinces they own in Africa that have ports), so I'm gobbling up more than I'd usually do. In the Balkans I'm a bit stuck as my ally Epirus has marched to the Danube and possibly beyond, has borders with now recovered Macedonia and the Antigonids, but has created a mess along the adreatic cost where I managed to erect Illyria and Dalmata as provinces with Epirote regions in between, only a singl anchorage alog that entire coast and gaps in my road building network as the Epirotes are not doing their thing. So if the Antigonids decide to go after me I will have to move troops oerland from Cisalpina and by sea from Taranto or Neapolis to Athens and from there overland into the Macedonia province which I adn't managed to grasp from the crumbling Macedonia in time. I short t's most likely I will have Antgonid forces in Dalmatia and Greece before I can assemble a countermove. Honestly, I think this game is lost, I'll make a backup save and either start over as Rome or try some other faction...