currently he’s terrified of all my older girls, my question is will he grow out of it?
My experiences raising cockerels with a mature flock where he will eventually take over as flockmaster is that several different things can happen.
The whole process can be fairly peaceful. No bullying or vicious attacks. One of the hens is dominant until one day he peacefully takes over.
Sometimes the more mature hens seek him out to do him damage, especially the dominant hen. Some people consider this to be schooling him or teaching him manners. I consider it to be brutal bullying but totally in character with some chickens. They can be bullies if they perceive another chicken to be weak. If he survives he will eventually take over. With the room you have I'd expect him to survive. The actual takeover may be brutal.
Fairly often he starts out forcing the pullets his age to mate. Sometimes the head hen ignores this, sometimes she knocks him off if he tries where she can see him. There is usually little fighting when this happens, he just runs off and she lets him.
At some point he will want to mate with the other mature hens. Some of the lower ranking ones may mate with him willingly (depends on his maturity and their personality) but the head hen and maybe other higher ranking hens may fight him off or just run away from him. Again the head hen may knock him off, even if the other mature hen is willing. Usually knocking him off is enough for her as long as he runs away.
Eventually the cockerel will mature enough to try to take over the flock from the head hen. In many of these scenarios that actual takeover can be pretty peaceful but it can also be pretty brutal. It depends a lot on the personality of the head hen and the cockerel.
Most of my cockerels take over as flock master at around 7 months age. Often it is pretty rough as they go through puberty but once they take over it is pretty calm. The earliest I had a cockerel take over was five months, he was pretty dominant and the hens were more submissive. I had a cockerel not move to take over until he was 11 months old. The head hen was pretty dominant and he had a fairly weak personality, I chose wrong with him. That was my bloodiest takeover. For two days he attacked her every time she approached the flock. They finally worked it out without either getting seriously injured. It could have ended differently.
I don't know what will finally happen with your flock, it could go many different ways. It is up to you to decide if you want a rooster and why. I think he has a decent chance to make a flock master but he may be totally unsuitable for that. Some just don't have the personality. Another option is that you decide you don't want to be bothered and eliminate him now and skip the drama.
Good luck!