SQL Server doesn’t really track index create or modification date by default
I say “really”, because SQL Server’s default trace captures things like index create and alter commands. However, the default trace rolls over pretty quickly on most active servers, and it’s rare that you’re looking up the creation date for an index you created five minutes ago.
I think it’s fine that SQL Server doesn’t permanently store the creation date and modification date for most indexes, because not everyone wants this information — so why not make the default as lightweight as possible?
That said, Kendra has several methods for answering the question of when a particular index was created.