Pilot reported a near miss with another aircraft shortly after being advised of an aircraft overtaking on the left by ATC.

Narrative

We departed PAO airport in VMC conditions with no ceiling and visibility greater tan 10 SM. We obtained flight following from NorCal Approach. We executed a right Dumbarton departure and connected with NorCal around VPKGO 2000 climbing 2500. NorCal shortly informed us a traffic was overtaking us less than a mile on my left hand direction altitude 2300. Within about 30 seconds of that traffic advisory; we observed a low wing aircraft fly directly above us approximately 100 ft above. We were not able to visually observe that traffic (we are high wing and the traffic was above); and we were not able to observe the traffic on ADS-B in either. It was a clear VFR day; and there were lots of traffic; especially along a common VFR departure corridor. When ATC provided the traffic advisory; we didn't have sufficient time to obtain visual contact with the overtaking traffic and make evasive maneuvers. I also assumed that ATC would provide a suggested heading/altitude to either/both aircraft that are on a collision course. This risk might have been reduced if: I responded 'negative contact' much sooner instead of 'looking for traffic.' And hopefully ATC would have given me an updated traffic location. We could also offset a popular departure corridor to reduce traffic conflicts. Periodically stopping our climb and do shallow banks so we can have better visibility above the aircraft. Do not depend on ATC for heading/altitude suggestions even if we have flight following.