I think if he’s not on the birth certificate, firstly he’ll have to go to court to prove the child’s parentage and then get put on the birth certificate. I don’t know much about this, but I’ve heard it can be relatively easy, depending on the circumstances. If you’re certain he’s the father and sure he’s going to apply to be added to the birth certificate, it may be worth just adding him in the first place. You can apply for child maintenance too then, if that’s relevant. It might look better for you too - the court is concerned with the child’s rights to see both their parents, I don’t know if you’d be seen as obstructive. I’d seek legal advice tbh.
But regardless, no court is going to award 50/50 custody of a newborn. The ‘standard’ is a couple of hours, once a week. Then as the child gets older, contact increases - so as a toddler, there may be a day a week, for example.
From my own experience, I was repeatedly told that the court didn’t care about how abusive he was towards me, they just cared if he was abusive towards the children (& even then, the threshold was very high - social services called the police after he assaulted our 7 year old, and the court didn’t care). I’m not saying this to scare you, just to warn/prepare you. Again though, it’ll be different with a baby.
I think the key thing to remember is that the court is basically acting for the child - their view is that the child has the right to a relationship with both parents, unless it can be proven this will have a detrimental impact on the child. The rights and wellbeing of the child is always at the centre of any proceedings.