The main things that increase AI Progress are:
Destroying Enemy Command Stations (10)
Destroying Enemy Home Command Stations (I think 100)
Destroying Enemy Warp Gates (10)
Destroying Enemy Special Forces Guard Posts (I think 1)
Losing Player Home Planet Command Stations (Or Command Station Cores) (30 for main, 40+ for the different levels of cores)
Losing Certain Player Capturables (Captive Human Settlements, etc) (often 15-30 or more)
Repairing/Rebuilding Golems (Expansion Only) (usually this works out to 100 or so for the initial repair, plus more on later repairs)
Detonating Warheads (2-3 for the smaller ones, 50 or more for the bigger ones)
Destroying Various Other Large AI Weapons (Astro Train Stations, Raid Engines, etc) (usually 1 or less, almost always 10 or less)
Glad you're enjoying the game!