The US Supreme Court is the most active of the federal judiciary courts?

No. The US Supreme Court has sole discretion over which cases it hears, choosing approximately 1-2% of the 10,000 or more petitions for writ of certiorari it receives every year.

The 94 US District Courts, which are trial courts and the point of entry to the federal judicial system, receive the highest volume of cases and are most active because they are required to hear most cases presented.