On TikTok there really isn’t a “trash” folder—you delete a DM and it’s gone from your account. Officially your only recourse is to submit a Data Download request (Settings → Privacy → Personalization and data → Download your data) and wait the usual several days.
If you’re on iPhone and you happened to back up to iCloud (or via Finder/iTunes) after that chat but before deletion, you could restore your whole device from that backup to get your TikTok data back—just be aware you’ll lose anything you’ve added since. Otherwise your best bet is asking the other person to resend or taking screenshots if they still have the chat.
(Quick Android note: with root you can sometimes dig into TikTok’s local cache to pull old message DB files, but it risks security and warranty—definitely not as smooth or safe as iOS backups.)