I've got more than a few styles of parallel LCDs in the shop.
The bulk of them power up to a cleared screen. A couple of them power up the way you describe, one of them powers up with random garbage all over the screen every time. It's probably got to do with how messy the power supply is or it's rise rate or...well, I don't care. As long as they 'clear' after they 'boot', I'm happy.

Are you able to display what you want to or does it come out garbage?