No, Many shows have publicized the 24 or 48 hour waiting period to report missing people but that doesn't exist in real police departments. As soon as you know a child or adult is missing, report it to police.
It is not against the law for an adult to go missing, so in some cases the police will not actively investigate without proof of foul play. You should still file a police report asap and take note of the police report number.
You can insist and request to speak with a supervisor. Look on their website, many times it states there is no waiting period to report a missing person.