They do happen super late, like 2450's which can make it feel that way.

I've had Andromeda invade so far with the Kelvin Empire, they arrived and asked to have a system of mine, I said no and they took it anyway and declared war. It was kinda funny as they didn't spawn in with a fleet right away so I just retook the system and waited before peacing out, but they do show up with a battle fleet every so often with GIGA powerful shields that have a special mechanic for the player to try and counter.

I beat them back and retook my system, after a while they tired again to take another but it gave me a chance to negotiate and such and such. They did end up taking an AI system at the galaxies edge and I presume if the AI wasn't silly trying to park it's fleets outside of it's original capital, they would go on to try and subjugate the galaxy with their mega fleet. (The situation report stated that up to 20,000 ships were coming, in small groups, so it looked like it was going to be a long term crisis with them attacking different sides of the galaxy.)

I'm trying to see if a Dominion or Undine crisis is going to spawn in my current game. I went poking into Fludic Space but as the Feds I just negotiated access with them? lol? But the Deep Space 9 events are happening for me now to eventually encounter the Dominion, so perhaps that will also be fun!

I'd love to set the Crisis way earlier, but I can't seem to control the crisis strength like in vanilla, so I am afraid that I'll just get 100 years in and get demolished by a fleet 1000 times my strength!

It's tied to the end game year in the game settings. So you can have them show up as early as you like. Set it for about 50 years before you want trouble to start. About 2300 would be my suggestion!