Couple ways:
- You could select the sound actor in the level and set its volume multiplier to 0 in the editor, and then set its volume multiplier to 1 in the level BP on Begin Overlap along with the Fade In.
- In the level BP, use a Stop node for the audio actor reference on Begin Play.
That should also pretty much answer your question of WHY the sound is playing when you begin the level; you never told it NOT to.