Depends on what you mean by push notifications.
Flarum comes natively with a Pusher integration extension, which you can enable and use immediately upon installation of Flarum. This puts the yellow bar on top of the All Discussions page to notify you of new replies and discussions.
You can also install other extensions.
There's a OneSignal integration here. Not sure if it's working on the latest Flarum version or not, though.
If you're on mobile, here is an Android/iOS app for mobile push notifications.
And a search on Flagrow.io came up with these and a few other push extensions you might want to take a look at.