Corporate jet First Officer reported receiving a low altitude alert from ATC departing VNY to the west. The First Officer noted that the rate of climb was too low.

Narrative

The weather was VMC; and we were given the CANOGA 3 Departure out of Van Nuys to the west. We initially set the altitude preselect to 1;750 for the at or below" restriction at 1.5 miles off the VOR. After takeoff; we briefly leveled off at 1;750 until past the 1.5 DME; and then transitioned into another climb. The altitude preselect was reset to the next altitude restriction of 4;000 ft. However; as pilot flying; my transition into that climb was not quick enough. As I was in the climb between approximately 2;500 - 3;000 ft. MSL; ATC issued a "low altitude alert." We had visual contact with the terrain and it was no factor; but at that time my climb rate was approximately 1;100 FPM. I increased my rate of climb and the flight proceeded without incident.Cause: Too low of rate of climb. Suggestions: Set the altitude preselect to 4;000 ft. instead of 1;750 for the initial climb; and plan the altitude restrictions as appropriate. Ensure the climb rate is appropriate; while not too low yet not too high."