In what order do Blueprints execute? Do they run in parallel?

Whilst figuring out the order of blueprint execution would be difficult, as it would require someone to poke around in the source code or experiment a lot, what I can suggest is that you attach a variable to the beginplay node of the gamemode/player blueprint, so that it will wait for the level blueprint to finish the task and THEN signal the character to continue.

This could even be moved to a custom event, that way it would not have to be on begin play. The level could do the heavy lifting at start, and then run a custom event on the gamemode or player character. That way you could control the order that the things happen in.