"Your DP is either
A a selfish prick who is leaving you to do all the childcare while he carries on with pre-baby life or
B afraid and overwhelmed by the sudden changes that the first DC brings into your life.
Probably the truth is somewhere in between, closer to A than B perhaps. He should not be going away on leisure trips IMO, and you should not be feeling guilty about your feelings towards him, they are amply justified. Of course he should find an hour in the evening to be together and you should be on the same page about how to find time for sex as soon as you feel the need. But you should also take him up on the "ask" question - it might not always be obvious when you need a break, I used to put the baby in the pram and take her out for a long walk, during which she would sleep most of the time, when ours were very small and DW needed a break."
This. Also @LannieDuck's suggestion of having periods during which he's the default carer is a good one.
Firstly, he needs to realise that he cannot just continue his pre-baby activities and he needs to stop his regular days and nights away. Time-consuming hobbies to a large extent get put on hold during the early years of parenting as does the previous social routine (though you will probably find you start to do a lot more day-time socialising with other parents of babies).
He may need things explained to him. My DH wanted to be helpful in the early months but needed to have things explained which seemed obvious to me. But when they were explained, he would do what was required. And except for going into work every day (no shared parental leave in those days), he was around the whole time.
In short, the way your partner is behaving is seriously not okay and it's not normal. He is letting you and your DD down badly. If he doesn't step up and start parenting, your relationship may never recover. So don't just rely on the passage of time. Make clear things cannot continue as they are, make clear to him what you need and give him the chance to step up. Good luck, OP.
But just in case he doesn't step up and you have to go it alone: yes, IME, things do get easier as your child gets bigger.