My sister was in a similar situation with her ex. They had broken up right after she got pregnant but before she knew. They remained friendly though. Her ex was at the hospital with us during labor, but really stayed in the background.
My sister didn't really need a lot of support during labor. Her water broke, she went to the hospital, they gave her an epidural and she slept until it was time to push. The rest of us kind of just hung out there. When it came time to push, she decided she wanted medical personnel only, no family in the room. We all knew this ahead of time but also knew that she reserved the option to change her mind depending on how she felt at the time.
We left the room for about an hour while she delivered and they let her hold him and clean him up. She wanted her ex to be able to hold him first so he came back in the room first and then the rest of us about 10 minutes later. He visited her at the hospital every day, but mom stayed with her at night and provided primary support after going home.
She gave her ex unlimited access to the baby in her house for the first two years and he usually stopped by after work for about an hour 3-4 times per week. Now they are slowly working towards Ex taking the baby for the day and overnight visits.
I am surprised at how well they have worked together and gotten along. It's all been pretty drama free. He pays her child support - max allowable in Texas - without a court order so I am pretty proud of them.
Sometimes relationships end and people are still able to be good co-parents. Congratulations to you and your ex for making that decision as well. Your child can only benefit.