Here's the start sequence for the 4 player version, Super Soccer. It might be similar.
Super Soccer reset (resized).jpg
Do you just need to manually advance the Player Unit once, or multiple times? If it's just once it would help to know what happens just before and just after the spot it gets stuck in. Each step of the Player Unit needs to accomplish something during rest and it will park there until that thing gets done (while the Score Motor keeps trying). Knowing which step it's stuck on might help sort out what the game is waiting for.

/Mark

Here's the relevant circuit from Super Soccer. It might be the same as yours.
Super Soccer Add Player (resized).jpg
The path in red is the main circuit used during reset to start a new game. One of the switches in that path may not be closing reliably.

I think the S relay is only active for the first Score Motor cycle during reset so the S relay switch on the right side is probably only closed for that first cycle. After that the P5A switch on the Player Unit should close for the rest of the reset cycle.

I'd start by checking the switch on the far right on the SB2 relay.

Thanks @rolf_martin_062. The Soccer schematic as subtle differences but is essentially the same:
Soccer Player Unit (resized).jpg
The Z1 and Z1 switches are replaced by switches on the Player Unit and the wire colors are different.