Tested 5 clients on my PC 3 times each. Times were more or less consistent on each run, biggest variation seemed for Uplay.
Setup: You are already logged in, there are no pending updates, you terminate client after each run (did not see significant time difference between repeated runs and 1st run after you log in), your logged in Windows account has admin rights so time is not wasted entering password (EGS and Uplay require admin rights to launch), time stops once launcher is usable.
EGS - 8 - 10 seconds
Steam - 20 seconds
GOG - 11 seconds
Uplay - 20 - 24 seconds
Heroic - 5 seconds
System: Ryzen 2600 with Samsung 970 EVO (2400 MB/s R/W as per Samsung Magician benchmark)
Really exposing the Valve fanboyism in the room. Steam genuinely takes quite a long time to start. People pretend it's quick because they leave it running, while cold booting Epic/alternatives and complaining.