Can a girl message a guy first?

Anonymous
My friend (female) told me over a couple of months ago that she has a guy for me to meet. We've since had multiple occasions where it didn't work out. He and I are now Facebook friends and I realized we're not total strangers. We've crossed paths on a dating app, worked together briefly a few years back, found out his mom was in my parent's wedding, and many years ago crossed paths for the first time. He's told our mutual friend he'd like to meet me, but her and I have very opposite schedules so it keeps not happening. With all this info, would it be weird for me to message him? Or should I wait for him to decide to reach out? I've always heard the guy should initiate, but this is a bit different.
Can a girl message a guy first?
3 Opinion