"Showing more commitment" is not a single act, be it standing outside in the rain or getting engaged.
That's fairy tale time. It's the prince climbing the glass tower for the lovely lady therein. It's not real.
Real commitment is massive, radical reorganisation of his life, right now, without any "commitment" from you, to acknowledge the fact he has a child in his life. And a subsequent reorganisation for you.
That means already rejigging his work schedule, not so that he "helps out" but that he takes on a good share of the parenting. Yes, really.
You shouldn't be needing to post here, asking for advice about a single, solitary task he can accomplish to prove things. He should be thinking of lots and lots of ways that he is changing his life to put you and the child into it.
With the emphasis on him doing the thinking, and the acting.
I think an engagement would be a way for you both to spin out this playing around for a lot longer.
He doesn't need some sort of trial period, or commitment pentathlon, he should just be doing it. While you get on with your life, rather than standing around, scoring the performance.
While you're busy doing that scoring, you're still hanging around, as an audience to his performance/life, instead of living your own.
Stop it. If he wants to "win you back" (hideous phrase), fine. It's not your problem. It's his. He's not "winning you back" at the moment, because you're making it quite clear he hasn't "lost you".
Seriously, put some effort into your own life - not his. You deserve it after hanging around for 8 years, and having given birth to, and raised the child of (yourself and) this strange, silly man.
Who seems to think photos in the office = fatherhood.