I've sent the gift from my giveaway but I got no response. What should I do?

Once week passed by you repick the winner.

Add the user on Steam. Find out if they received your email. Some users still have the wrong email address entered on this site.

In future, first send an email asking them to confirm the address is in use. If you don't get a response, you don't lose the key.

see if the game is on their profile on steam. if so get support to flag as received.

as told by members here, contact support. they will help.
for future, always contact winner via steam and/or email and verify identity, then send the gift.