Optics aren't great for your dss either.
At the moment, he is an adult who rashly packed in his job, returned to mummy's sofa an hour away from his baby, knowing he had no independent means of transport.
Pulling his weight as a dad right now means taking responsibility, finding a job, securing a place to live, paying maintenance, and then working out the best way to co-parent. How can he expect to take a newborn overnight when he does not even have a bed for himself?
For now, the most realistic approach is for him to see the baby regularly, even if only for shorter periods, until his circumstances stabilise. This will involve a lot of commuting, and since he is not currently employed he has plenty of time to do this so should not be an issue. It is a temporary step until he gets his life in order.
If he cannot reach an agreement with the mother, the next step is mediation or court for formal access arrangements. He was responsible enough to bring a child into the world and needs to step up and be responsible enough to resolve childcare arrangements properly.
Failing to do so risks him becoming just another feckless dad. You can't/shouldn't do this for him, sign post him but he needs to drive it from the beginning.