Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Airspace Structure; Human Factors; Procedure
Assigned the WLKKR3 Departure; CVS [climb via SID] except maintain 4;000. We were doing the noise abatement takeoff; and leveled at 1;700 for the restriction. While in the turn to heading 210; SOCAL assigned us climb to 6;000. PF (Pilot Flying) initiated a climb up; however SOCAL issued a low altitude alert and suggested we increase the rate of climb. PF increased the rate of climb up to 6;000. Rest of the flight uneventful. Start a more aggressive rate of climb to avoid low altitude alert on this departure.
Air taxi First Officer reported receiving a low altitude alert from ATC shortly after departure.