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.