You can use -ANR to search using Ambiguous Name Resolution (so you can type their first, last, username, etc), but while ANR will match a user’s primary email address, it will not match their other SMTP aliases. ANR can return multiple matches (so ensure your code handles this case).
For email address:
get-mailbox -Anr user@domain.com
For public folder email address:
Get-MailPublicFolder -Anr user@domain.com
– Pouyan