I'm a parent, just at the start of that journey really, certainly I have a lot to learn and I'm sure I'll make a lot of mistakes.
That said, it seems like quality time and shared interests is foundational. Like if you watch her ballet class every week (not playing on your phone) then I don't think she will care very much about a missed birthday and certainly not interested in a happy birthday from the team.
I doubt I'll have time to go to every ballet class but I'll sure as shit try.