Does regex work on timestamp?

Regex requires a keyword field as far as I know and does not mapped on fields mapped as date.

Yes, storing it as a keyword field should work, but then you can naturally not use it as a date filter.

It is probably mapped as a date field, so the mapping is the first thing to check.

You could consider keeping the field mapped as a date field as this is useful for range queries and then additionally extract the time into a separate field mapped as a keyword. That would allow you to search by string range instead of having vto use a more expensive regex query.