Does a justice have to be at least 30 years old to be appointed to the US Supreme Court?

No. There are no constitutional age, residency, citizenship, or educational requirements for justices of the US Supreme Court. In practice, however, most nominees are in their late 40s, 50s, or (sometimes) early 60s, so they've had time to develop professionally but can still contribute to the court for several decades.

The youngest justice appointed to the US Supreme Court was Joseph Story, who was 32 years old when he was seated in 1812.