Richard Sherman -- GF Gives Birth ... Russell Wilson Offers to Babysit

Finally, some good news for Richard Sherman -- his girlfriend just gave birth to a bouncing baby boy ... and Russell Wilson has already offered to watch the kid.

Sherman's GF Ashley Moss was on baby-watch during the Super Bowl -- and there was a (slight) chance the kid could have arrived during the big game.

But the baby waited it out ... until this morning ... and Richard made the announcement just a few hours ago:

"My son sure does know how to make an entrance! 2/5/15 ... Is it a coincidence or is he just that clever?! Either way I'm ecstatic."

The 2/5 thing is a reference to Sherman's jersey ... #25.

A short time later, Russell tweeted at Sherm ... "so happy for you bud!!! You are going to be an amazing dad! Love you bro! Let me [know] if u need me to babysit!"