I will be going SJC-LAX on American, connecting to a Cathay Pacific
flight LAX-HKG. Is there a way to make the domestic-to-international
connection in LAX on the air side of security, or will I have the
pleasure of meeting TSA agents at both SJC and LAX?

Airside connection at LAX? Ha. Ha, ha, ha. Gasp, choke. Uh, no.

AA arrives at T4. CX leaves from the international terminal. The
terminals are adjacent to each other and it's much faster to walk
than to take the bus because the roadway is one-way the wrong way
and the bus has to go all the way around the airport.