My wife is a nurse. I was a clerk, but at her suggestion - due to her making more than me - I am now a stay at home dad and she is the bread-winner. Things are tight, but nobody goes without anything, and we still manage to find enough spare change to have the occasional date night.
Part of our conversation prior to having our baby (who is now 15 months old) was finances and if we were ready. I told her we could plan and prepare forever and always find reasons why now isn't the perfect time. There is no such thing as the perfect time. It's like waiting for the perfect cell phone, or the perfect house. There will always be a caveat.
So long as you're not in debt and can reasonably assure your income for the foreseeable future, there's no reason not to.
The one thing we did was open up a joint account that neither of us touches and put money in it for the baby. That's her money, not ours. We only make deposits. We have our other joint account for bills and emergencies and such, but they are completely different banks.
My only suggestion is to start behaving as if you have some debt. Spend a little less on take-out. Pinch a few more pennies here and there. See which bills or spending habits you can be a little more economical with now, because babies are expensive. Also find out what parental leave is like for your area. This was a fairly stressful moment for us, as my benefits at the time were better than my wife's in that regard; I didn't quit my job until a few months ago partially due to this. If you need to start setting aside money now so she can take off some extra time for recovery, that's something you're better off being aware of ahead if time. As it was, my income was able to keep us afloat until she was back to work, and we didn't have to change much about our lifestyle (other than adjusting to caring for a whole other human being). And that was with her pay cut catching us by surprise. Laws had just changed regarding parental leave in our state, and so even our HR department didn't really know what was going on. Things were... Weird for a little while. If you can avoid such surprises, it'll make everything much easier to manage.
The last thing I can say is, enjoy all of it. It's a hell of a change no matter how much you mentally prepare yourself, but if you do it with love and joy, there's nothing better in this life than being a parent. Best of luck, friend. ❤️