Nap time is a good time to get some work/learning in.
Although when they are 0 to 6 months old it can be pretty exhausting. I once was so sleep deprived I showed up to work with one black and one brown shoe when mine was a couple months old.
I would recommend getting up an hour or two before your family and settling in for some time to learn new things and work on personal projects. This can also work in the evening or both.
Ask your spouse to trade up for some free time for each of you maybe give each other a two hour block of time on Saturday and Sunday.
Do you watch TV, give up a TV show or go down to one show and use the rest of the time for personal projects if you enjoy doing that.
Everyone needs downtime, and learning working on a side project is fun for me. But take time for hobbies too.
And prioritize spending time with your family. Kids grow up fast so make the most of your time with them. Don't try to work/learn when you're supposed to be spending time with them.
I think that's why getting up an hour or two early are some of the most productive hours of the day. No one else is awake in the house, no emails, no phone calls.
Good luck carving out some time for yourself.