https://www.trainerroad.com/forumt/training-as-a-parent/
Some of what you mention was discussed above.
From my own experience, I have just started back on SSB low volume 6 weeks after the birth of our 2nd child.
I train in the evenings mainly as early mornings after little sleep would be too much for me and would mean my wife has to be the sole carer at those times which is a little unfair. I think somewhere around 4-6 weeks a baby’s sleep can start to improve and by 2 months they should have developed a more regular pattern.
Advice: talk to your partner about their goals and give support for them to get back into a routine too.