Heavy Transport
Flight Crew Air Transport Pilot (ATP)
Situational Awareness
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
During climb out from runway 21R we were flying runway heading and cleared to climb to 10;000 feet. At about 3;800 feet ATC advised us of traffic at our 12 o'clock position and no altitude readout. At about that time we were showing a proximate traffic symbol on the Nav Displays. ATC then cleared us to turn right to a heading of 230' and again reported traffic at our 12 o'clock position. The proximate traffic symbol on our Nav Displays showed the symbol to the left of our Nav Display Track. I was searching for the traffic from our 11 o'clock to 1 o'clock position above; at and below our flight path. It was then the High Wing Single Engine Tailwheel airplane came into view at our 1 o'clock position about 500 feet above our altitude flying from right (North) to left (South) direction. I then took control of the aircraft and pushed hard forward; nose down; to stop the climb and initiate a nose down to below the horizon to avoid the High Wing Single Engine Tailwheel airplane of which we did by about 300 feet. In my opinion if we had not taken this evasive action we would have hit the High Wing Single Engine Tailwheel Airplane. The pilot of the High Wing Single Engine Tailwheel Airplane in my opinion did not see us because he took no evasive action. We advised Travis Air Force Base Departure Control of the near miss and then continued our climb and heading as previously cleared. We were then switched over to Oakland Center and also advised them of the near miss. After reaching cruise altitude I then satcom called [company] Dispatch/Operations and advised them of the near miss.
Suggest being able to use close in noise abatement departure procedure to be able to climb out at slower airspeed and to be able to get above the VFR traffic sooner.
A flight crew reported an NMAC with a light single on departure from SUU.