Im an SWE, and luckily I have the option to work completely from home. That helps a lot. Some time I would stay awake all night coding, and monitor my son when he got sick, so my wife can sleep. Then i would sleep a bit when she wakes up in the morning.
With a baby, you are constantly moving. If Im not coding, and then I play with my son or making food for him. The concept of “me time” is 100% vanished. Since my son was born, 3yrs ago, me and my wife only go to cinema once to watch The Arrival. And she didnt even like it lol.
Be prepare mentally and physically. Its a wild ride, that bring out a lot of emotions in you. But it is also fun and rewarding. Good luck!