It is possible for a VisualElement to transition from one IStyle state to another using transition properties. However, I have not been able to figure an obvious way to make an element animate its initial appearance on-screen, for example to fade-in when first displayed or animate its position coming up from the bottom.
This still has the issue where you need to set up the element in it’s hidden state in the UI Builder, so when it loads it can then immediately be shown. Which is obviously non-ideal.
The only other solution I can think of is to, in code:
set transition time to 0
apply hidden styling
set transition time back to whatever it was before