"It was so awful. You weren't treating me like the centre of the universe so I sadly went to work where I was so sad I couldn't see where I was going and I tripped over because I was so sad and sadly my dick just fell in to someone's open legs"?????????
I'm so sorry, OP. My exh cheated when I was pregnant (I didn't understand him, apparently), so I can empathise a little. It didn't just happen and the woman he did it with wasn't just lying there with her legs spread on the off chance someone feeling sad would come along and 'neeeeeed' her. There would have been flirting, secrecy, meaningful looks, the whole sheebang before it happened. He knew. He absolutely knew what he was doing and it was absolutely not a spur of the moment, couldn't see it coming 'mistake'.
4 weeks is no time at all for you to get your head around this, and that's without being solely responsible for a small baby. There is no need at all for you to make decisions about the future at the moment and he will just have to accept that. And you need to stop feeling guilty. You don't know what to do because, at the moment, it's not clear to you what to do. So don't 'do' anything. Carry on as you are until you are in a much stronger, less shocked, less sleep deprived situation and then see what you think and how you feel. And it's fine to get bloody angry too - he has tainted these first precious weeks as a mother for you and you won't ever get to do them again untainted. Get really bloody angry about that.
You call the shots now and you don't call them until you're good and ready. Just to reassure you, if you're anxious about managing as a single mum (although you already ARE managing!), I raised ds alone. I didn't go on benefits, I worked full time, I kept my house, he went to a fab nursery, and I've even got to a position where I can afford to privately educate him if I choose to do so. Being a single mum is tiring but it is also the most rewarding experience of my life. It didn't blight it, it wasn't 'benefit street', grungy flats and Jeremy Kyle. It was also a HELL of a lot easier doing it by myself than trying to parent a self-pitying, selfish, whining man-child with a sense of entitlement the size of a family car alongside my ds would have been.
Whatever you decide, whenever you decide it, I promise you that this situation is not a disaster. Just manage the day to day for now.