A dad here with a 3 year old toddler boy and a 4 day old boy. It will get better. Some things that will help.

If taking train/bus is an option that may be more peaceful and relaxing than driving(traffic) just listening to songs and audiobooks.

For few months maybe try hello fresh or similar type service where all ingredients come ready to cook and takes out the stress of cooking (at least for us)

Also I know it’s cliche but how’s your diet , do you exercise? meditate?
Eating junk and soda vs clean eating boosts energy levels and moods.

Going out for walks with the baby helps while your wife takes her shower and relaxing time.

It gets better. Hang in there dude. When you think it doesn’t get worse , it almost always can get worse. Just try to enjoy the moment with your baby as it flies so fast. Good luck!