One factor that seems to be a theme in your examples… when an event is attached to a sound (the jingle) or a specific sight (looking at the page number on your book) it often ‘holds’ a little better.
Your first day of school was a big moment, but there probably wasn’t a singular anchoring experience to remember it specifically. (But do you at least remember how you felt? Excited, scared? Liked it, or didn’t like it?)
As for your dad’s birthday, it seems important, but you don’t have a visual to anchor the exact date. You’d probably be able to remember it better if you wrote out on a piece of paper “Dad’s birthday is on the (whatever the right date is)” and looked at it for a few days, it would ‘lock in’ better, because you’ll be remembering what you saw instead of a fact or idea/experience.
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