My wife took unpaid leave for 6 months when the baby was born - she was managing the baby on her own when I was at work. She used to be exhausted all the time - the baby never let her sleep more than 2 hours at a stretch. So I made it a point to be back home as soon as possible so I could help out - at that point, I really didn't have any time to do something for myself. Neither of us did. This changed as the baby got older.
So it really depends on your home situation. If you have grand parent support, it may be easier. If you and your wife are on your own, as we were, then getting time to yourself in the first few months is a rarity. Sorry if that isn't what you want to hear

However, if your bike commute time and your driving time are almost the same, you may be able to continue.
On the plus side - my son really likes it now if I bike him to school. My current situation doesn't allow me to do that often - but I do it when I can.