Ultimatums can work, IMO. You’re forcing the issue, but your partner still has to make a choice.
I made it perfectly clear to my then partner that I wanted to get married within a certain time frame. I didn’t get a proposal as such, but we agreed to get married, and bought a ring together.
He showed very little interest in the wedding planning ( but I know some men can be like that ), but then 6 months before the big day he told me he couldn’t go through with it, and just wanted to carry on living together.
I left him, and went to my parents, because I knew that I wouldn’t be happy without being married. Less than 24 hours later he showed up at my parents, told me I was the best thing that ever happened to him, and from then he threw himself into all aspects of the wedding planning with great enthusiasm.
We’ve now been married for 21 years.
I can remember feeling occasionally in the early days that we were only married because I forced the issue. But then I realised that it was still a choice he made, just as I made a choice to leave rather than just live together.
OP, I know that it’s more difficult because you have a child together, but if he doesn’t want to get married, you still have choices you can make .