The safety of you and your baby must come first. Speaking from first hand experience, the situation will not improve on its own. If he refuses to seek treatment the situation will only worsen..putting both yours and your child's safety in jeopardy.
I have PTSD. My ex-husband did NOT have PTSD, but did have some mental health issues (mostly very severe depression that included some outbursts of rage). When we first started dating the outbursts were infrequent and when they happened it was yelling and property destruction. He never came near me with his anger. I was aware of the situation. He was embarrassed and ashamed of his behavior. He was getting treatment (both therapy and medication). I was willing to accept him as a flawed human being who was truly a kind, compassionate man with some problems that he was working very hard at overcoming. Over time his behavior worsened. He would do the thing you described of getting only inches from my face while screaming, red-faced, at the top of his lungs. He would back me into a corner while screaming and yelling at me. While these incidents were still infrequent they were increasing in frequency. Through all of this we got married and had a child. He seemed to be doing okay...still bumps in the road from time to time but okay. Then came the day when I was at the dentist and he was watching our daughter at home...she was 2½ years old and he beat the crap out of her. Fortunately there was no long-term physical damage. I made him leave the home, reported it to his psychiatrist, dept of children & families, etc. Like you, I still wanted to support him and keep our family together. We spent the next year with him living out of the home, receiving intense therapy, parenting classes, anger management classes, etc. When we thought things had improved and he was ready to handle it, he moved back into our home gradually...a couple days a week, then three days at a time, etc until he was living back at home full-time. Almost exactly one year after the original incident he hit our daughter again. Not as severely as the first time...I was at home but in the next room and came running to intervene. After that I kicked him out and filed for divorce.
I'm not saying it has to end like that. But my ex-husband really was a good guy. He still is a good guy. Despite his best efforts, he just cannot guarantee that he can remain a safe parent. He only sees our daughter with supervision. He understands this, doesn't argue it and knows it is the best thing for our daughter.
What I am saying for you is don't think it will get better without treatment. We had lots of treatment and things still didn't get better. Don't think it is safe to live with this man if his PTSD and anger issues remain untreated. You don't have to completely cut him from your life but you do owe it to yourself and your child to set healthy boundaries.