SCT TRACON Controller reported working a departure aircraft that was responding to a TCAS RA resulting in flight below the MVA. The controller issued a heading and altitude to the aircraft that was clear of traffic and the flight continued to its destination.

Narrative

I was working Harbor sector which has departures off LGB airport. Aircraft X departed; there was a lot of VFR traffic in the area that wasn't talking to anyone and some that had just departed LGB. Aircraft X departs LGB keeps him for a little longer; I imagine is to try to deconflict from traffic. LGB calls and says we are stopping Aircraft X at 020 and then they ship him over. As soon as I talked to Aircraft X I gave a vector away from traffic. Aircraft X reported responding to a TCAS RA and climbing. Aircraft X didn't climbed much since there was an aircraft at 030. I saw a descend to 019. At this point Aircraft X entered a 027 MVA. The heading I issued was clear of traffic and Aircraft X was able to climb to 070. I keep saying this but if we don't fix this; we will have a midair here. If one of those targets doesn't have a transponder or Aircraft X gets the wrong frequency or TRACON assumes tower is doing something or vice versa. There's too many was this will happen. If they are modernizing things lets modernize the airspace around airports. LGB needs some airspace protection around the departure area. Also LGB tower needs more options for headings. They could use headings as far as 270 to 180. This should be an easy fix through LOA.Create airspace around LGB to protect arrivals and Departures. A class C would help or an extension of class B. Better procedures with headings that LGB is allowed to issue.