is it possible to figure out the time and date an ios update was made to my phone?

I'm not aware that there is any way to know this once the update is installed.

Doesn't change that I don't believe there's any place to see the date it was downloaded.

It might be logged somewhere, but I don't know of anyway to display anything like. It might be available in an Apple diagnostic.

Unless something went awry during installation there may not be a log of it.