From your post, this doesn't sound like a one off, but more a regular thing. How have you addressed this with him in the past months? I'm guessing you would have already told him your thoughts and concerns, but he's not listening and carrying on without so much as a care for your feelings. That's a big red flag.
You posted that you're feeling stuck. I get that. I was in your place once. XH was an alcoholic. When I met/married him he wasn't: you couldn't have met a nicer and more decent bloke. Unfortunately an RTC (which caused a life long injury) a year into our marriage (and a month before DC was born) put paid to that. He went down the path of alcoholism and drugs. Unfortunately I didn't spot it right away (I was focussed on the injuries he had and the healing/rehab from those). When I did spot it, and started to get him the help he needed, it took me bloody years before I figured that the only person who could help himself was XH. And he had to want to do it, and keep sticking with getting the help. He wasn't engaging with the help and basically gaslit me for years. I also learned that it was ok for me to put in boundaries, stand by them and leave (that was thanks to a thread I saw on MN some years back). Our marriage didn't last 7yrs (he also fucked off with OW as a final nail in the coffin). When he's sober, you wouldn't meet a more lovely guy....but when drunk, he's a monster. It's heartbreaking and tragic, but a living nightmare when you're in the thick of it. I didn't divorce him for the injury or the fact that he wasn't working: I divorced him because of the alcoholism/drug taking (and all the abusive behaviours/shit that comes with that).
What's your current situation? Married or not? Any other kids together? Do you work/are financially independent of him? Do you live together (rent or own a place together)? Do you have supportive family and friends nearby?
I think: figure out logistics and practical things. Make a decision going forward that is best for you and your baby. If that means that you end things with him, then do that. Make plans and do it sooner rather than later.
If you're not married, then don't register the birth with him (i.e. have his name on the birth certificate), do it on your own. If you're not married and you register the birth with him (i.e. he's named on the birth cert), that would give him Parental Responsibility - i.e. the same parental rights that you'd have. You really don't need that shit with someone who is an alcoholic/drug user. He'd legally have a say in contact, school/nursery choices, healthcare decisions, where you and DC live etc. He'd be able to pick DC up from school/nursery without your say so, not return DC to you and it would be completely legal/in his rights to do so. I had to go to Court for a Prohibited Steps Order to prevent XH from doing this and having unsupervised contact with DC (due to his alcohol and drug use). The Judge luckily saw through XH's nonsense (and abusive behaviours towards me) and not only granted that, but Judge also immediately put in a CAO at the same time (which stated the DC fully reside with me, no overnight stays with XH, and that I had complete control over contact).
Trust me on this, I should have ended things way before I did (though as we were married, XH would have automatic PR anyway). He's not listening to you, and he's not respecting you (or himself for that matter). He is showing you contempt and showing you who he is by doing the same actions and behaviours each and every time he binge drinks (and does God knows what else). My XH had a family, a marriage, a nice home. I was the breadwinner (in order to allow him to rehab from his injuries and get his head around what had happened to him), I paid for private residential rehab for him (for the alcohol/drugs). He treated that all with contempt and didn't lift a finger to make the changes. He's now on his own. Please don't condemn yourself and a child to this sort of nightmare.
Don't let your partner blame the alcohol for his behaviours either. If his behaviour changes that bloody much when he does drink, then he should be adult enough to think, "shit, this is causing a problem...I'll stop drinking/limit myself to one alcoholic drink". No one forces him to drink, he does that of his own free will. I understand having stress at work, or being worried about parenthood - I think most of us have worries and stresses in our lives - but we don't all hit the bottle/drugs, do we?
I know my message sounds very doom and gloom-like, but I'm telling you the truth, and it isn't pretty. I don't hate men - I know plenty of really lovely, decent, respectful guys (who are my friends, colleagues and family). I'm just telling you the reality of living with someone who has an alcohol/drug problem, and who doesn't accept/listen or address the problem.