The reason he does not appear in any database is by design, and the law is explicit about it.
Juvenile records and placements are confidential regardless of age. The critical factor is not how old someone is right now but how old they were when the offense occurred and when the case was adjudicated. If he was charged and processed through the juvenile system before turning 18, that case is sealed from public view even after he turns 19. Juvenile correctional facilities refer to their population as residents rather than inmates, and their locations, records, and status are kept entirely private under state and federal law.
The reasoning behind this protection is that the juvenile justice system is built around rehabilitation rather than punishment, and exposing a young person's record publicly would follow them into adulthood and undermine the entire premise of the system. That protection extends to the people who want to find them, regardless of the relationship or the reason for looking.
If you have a legitimate reason to contact this person, the options are limited but not zero. If you are a family member, the facility may allow contact through official channels at the discretion of the administration. Reaching out to the facility directly and explaining your relationship and reason for contact is worth trying. A family court or probation officer connected to the case may also be an appropriate point of contact if the relationship warrants it.
If the connection is more personal than familial, the path forward is narrower. Writing a letter to the facility asking that it be forwarded to the resident is sometimes possible, but the facility has full discretion over whether that happens.