Well, we didn't have a newborn and "soon to be married", but been together for a long time.
If it was good before the happening and he takes all the blame, then I'll try to work it out if I'd feel it at the time(with counseling and if he makes all the right noises). But it doesn't mean you can't change your mind even if your, let's say a year or two down the line.
If it was bad before the betrayal and right now you are affected by pick me dance and life changed that a newborn brings, then it would not be so clear cut.
If it wasn't good at the beginning, it ain't going to be good now. If you think that from year or two from today when he's going out you'll be wondering what he's up to, then no. And when you go ahead you'll have to be prepared that he's going to do it again, because you can't really trust him to the end and back.
I really do get it, I forgave but I never forget and my circumstances weren't as complicated as yours. But I did it for all the wrong reasons. I was afraid, I never knew a life without him. I would like to think I'd do better if there were children involved, because then I'd have do be strong for them (for them not seeing a dysfunctional relationship), but I've never been in that position, so it's only guessing.
Whatever you do, if you go with it for now and make peace or if you decide something else in year x, it's going to be alright.