When my wife applied for her call, K5KKD, I found it by typing it into
Google.
The first hit took me to a site that listed recent and pending FCC Vanity
Call actions.
It showed the date the call would be issued, and sure enough, it appeared in
the FCC database on that date.
Unfortunately, I didn't save that link, so I have no idea of the URL, as
that was over a year ago.