Welcome to Pinside!
I'm still / always learning myself so someone may feel free to correct me if I'm wrong.
During attract, the "game logic" that looks for most switch inputs is not running. The game is looking for start, diag, and ball-locating switch inputs, but should ignore all else in "attract mode". When you start a game, the "game mode program" logic runs so now all switches are read, and any stuck switches are fair game to fire all at once.
If you have stuck coils during attract mode, that means the driving circuit(s) for the affected coil is defective "always on" at the board level. But that doesn't seem to be what's happening here, so that's good. It's far easier for a newbie like yourself to look for the visible mechanical issues than to troubleshoot boards.
So yes, you may have a stuck switch telling the game to fire the coil as soon as "game mode" starts. (It's also possible in some cases for the switch-reading circuitry on the boards to go defective, but that's relatively uncommon so let's not worry about that for now).
Do you have the manual for the game? It will be very useful, even if the diagrams don't make any sense at first glance. If you don't have it, go to ipdb.org and look up your game, you can download most manuals from there.
One thing you can try, is unplug connector 1J19 from the MPU board (upper right corner of the board, 2nd connector down from the top). With that connector removed, the coils for the pop bumpers and slingshots will not lock on. You can then put the game into test mode, go into the "switch test", and see which switches are stuck. If the pop bumper switch shows up in test, investigate further.
That left pop bumper is especially tricky because of how tightly everything is crammed nearby. I rebuilt it once and would suffer intermittent meltdowns due to a sporadic, intermittent short in the switch that was almost invisible to the naked eye. I could tell it had been troublesome in the game's previous history due to hints of other repairs. Make sure there is no way that any metal from the switch can EVER touch ANY metal on the pop mechanism... even a "few hairs' width" is too close. Also make sure you have the trigger leaf on the switch on the proper side of the pawl... it's an easy / common thing to mess up.
Space Station is a great game, worth debugging for sure.