Ah, got it. Right after I append the HTML to the DOM I run this on all the inputs I’d like to have a datepicker pop up with. Datepicker adds a class to elements it has been attached to, so we can filter out existing inputs and only apply it to new ones.
$('.date').not('.hasDatePicker').datepicker();
I hope this helps people as I was Googling for days and didn’t find anything!
You should also note that it would be faster to check for input.date in the new generated HTML by setting that as a context, rather than the whole page, as it will save time, due to this being a more efficient operation.