I don't think it's unusual for men to be shocked by the demands of raising a child. It happens to some women too. Basically it means putting another human being first all the time, no matter how exhausted you are.
For a relationship to survive having a child, it needs to be rock solid, so it is no surprise that many relationships fail. You aren't the only one so stop beating yourself up.
The past is the past so all you can do is look forward. You haven't lost your baby, but you need to be realistic about what you can cope with. I guess you work 40 hours a week in a job and she looks after little one for those 40 hours. Then there are the remaining 128 hours in the week, which you both need to work out how you will share/cover between you.
While very small, you will need to travel to her to see your baby. Can you travel there, maybe two weekday evenings a week to do 'bath & bed' and a few hours at the weekend.
Let your ex teach you how to care for your little one, if she is willing. it is a skill you need to learn before you can care for your child on your own. It isn't easy so take your time. With parenting, routine is good. Aim for a routine that you stick to, and everyone knows what to expect.
As long as your little one knows you love them, and are there for them, this is just a minor hiccup, You can still be a great dad. xx