In BTK they had crime scene DNA and Dennis Rader name but not his DNA. They learned his daughter was a student at Kansas State. They checked with the on campus clinic and discovered she had a Pap smear on file there. Search warrant was granted for DNA testing of the Pap smear.
And that’s how it should be. If you volunteer to have your DNA on a public database for all to see, no warrant should be needed because you gave permission. If you put it on a private database - search warrant. If you have a sample on file somewhere and they want to look at it - search warrant. Search warrants take less than ten minutes to get by phone in most localities, so there’s no reason for them not to get one.