You have to remember that posters dont have the correct answer for you.
They can only give their uninformed opinion, or their personal experience of a similar circumstance, which won’t contain the same variables as your situation.
Even posters claiming to be cafcass officers or similar (because if they are, they shouldn’t be compromising their professional integrity by commenting on a public forum on the subject).
My experience is that abusive absent fathers generally can’t be bothered to chase up custody. They use the threat to control your fear.
Like mine, he may not even want to pay the solicitor to start mediation proceedings or turn up to the first appointment even.
As soon as they realise access means a cut of their income towards child support, they back down too.
My children’s absent father had put me in A&E, punched me in the head, thrown me around the room, locked me out, yammed the baby into her chair, thrown a toaster sized rock at me whilst I was holding her and so on, but he’s still be entitled to access.
Keep a record of ebry communication you have with your ex partner, try and make sure it’s all in writing - emails or texts - so you have a ‘paper trail’ to refer back to.
Ultimately, it will be a year or more yet, so no immediate worry. The ‘little and often’ contact is manageable for you. You can be present whilst he’s with baby, in a supported or supervised environment.
Ensure you ALWAYS make plain in written communication to him that you encourage contact. It shows you are supporting the best interests of the child, even if you don’t actually think that’s correct.
Don’t volutarily put yourself in the system. He might just get bored eventually and not bother requesting access. If you start the ball rolling by instructing a mediator or solicitor, it’s out of your hands.