Significant other not letting me bond with baby?

Now that we’ve had our baby (4 days ago) my SO has become controlling over our baby and won’t let me do certain things with him on my own. Every time I’m changing him my SO rushes over to do it, or every time I feed him he does the same thing. He won’t let me carry his car seat, or EVER be alone with him. He was supposed to go back to work on the first day but now he’s making excuses as to why he can’t, he’s treating the baby like a new video game and is trying to take him to friends parties and show him off at 4 DAYS OLD!

My SO can be competitive and I feel like he thinks he needs to one up me all the time. My bond with the baby is severely suffering because I don’t have any time with him. The fact that I’ve never been alone in the same room with my baby or even had a moment with him without my SO trying to take him away is making me want to give up.

Has anyone else gone through this before? I realize everything is still new and things may change but this is seriously making me consider leaving him and sharing custody because I know I would get sooo much more time with my baby.