The first few months of new parenthood is awesome and also a blur. Personally I'd put cycling on the back burner for a bit and not worry about it. Just enjoy the time with your new kid and try to get some sleep. Ride when you can, but don't beat yourself up if it's not happening. After a few months things will level out, your baby will start to become more fun and everyone will be sleeping normally, and you should be able to get back into a routine.
As a new parent, I definitely gravitated towards more indoor riding, finding time in evenings or early mornings during the week to get rides in. I'm 7 years into this parenting experiment, and my weekend time in particular is still very crunched, more so now than when my child was first born. I still find time to ride (and race) but it's not always easy. There are lots of scheduled weekend activities in our house that definitely eat into bike time. I'm fortunate to have an awesome partner who understands and encourages my cycling habit. I also now have a 7-year-old who loves riding bikes, which is awesome because it means I can spend Saturday AM riding with my training group, and Sunday AM riding with my kid at the local park, pump track, MTB trails, etc. Everyone wins.