I havd 2 kids, one aged 5 and one is almost a year old.
I still have a decent amount of gaming time. I can probably play for a few hours a day, and more on weekends. It comes down to planning and prioritizing your free time. Some people are exhausted after the day and spend an hour in the couch in front of the telly - I just game instead. Some go for a walk (I should probably do that) but I game instead.
My usual day looks like:
05:30 - get up, go to work
14:00-15:00 - pick up kids (wife delivers at daycare before she starts work at around 9), go home and take care of them
16:00-16:30 - wife comes home from work
16:30 - 17:30 - usually I take an hour here to game
17:30 - 19:00 - I shop, prepare dinner, eat dinner, cleanup dinner and so on - this is my responsibility each day since wife does the laundry.
19:00 - 20:00 - kids are prepped for bed, and after the prep wife will put the small one down. My 5 year old stays up for a little longer but usually just plays in her room at this point.
20:00 - 22:00 - papa gaming time
22:00 - go to bed
Now remember - when you have kids, life is messy. Some days I don’t game at all because we decide on a family outing, some days a kid gets sick and needs you 24/7. Some days, wife gets sick and you have 24/7 responsibility of everything. However, I always aim to get at least an hour or two of gaming time each day, because it helps me relax and recharge.
Also - remember, that when you spend time with the kids, just be present. Don’t watch forums on the phone - spend time with them, because then you won’t feel guilty when you go dedicate some gaming time.
Now my 5 year old is showing an interest in gaming, so sometimes we play together. We have been playing on the Switch system (games like Pokemon, Overcooked and other co-op games) and when she gets older who knows - maybe she will join me in WoW or whatever, so you can both game AND spend time with your kids.
No matter what - don’t feel guilty for wanting time to game. Prioritize your day, make sure you do your responsibilities, spend quality time with kids, and then take care of yourself too. As a new parent, your life will be a freaking train wreck, but eventually you will figure out what works for you and your family.
Best of luck - having kids is the best thing ever, but also the hardest thing ever. But “just” having a child doesn’t mean you should give up every hobby you have - you might just have to dial it down for a few years.
Hope this helps, and best of luck to you and your family.