Why is Animation Blueprint Update is called before Begin Play?

The tool tip reads “executed when being play is called on the owning component”…
Is Begin Play called in your owning component?

Ether way, as per the tool tip Begin Play is not where one would initialize things. Just like Begin Play, this is not supposed to be where where you initialize things.
Normally, you override the construction script to take care of initialization and storing of one-off calculations.

Either way, you should probably file a bug report here.
In my brief test with a print string I have the following stack
Update Anim
Anim Begin Play
Character begin play

that’s just off, going by their own tool tips…