General Aviation pilot reported an inadvertent entry into IMC and a momentary loss of aircraft control during initial climb. Pilot became reoriented and with ATC assistance was able to safely exit the area and continue to destination.

Narrative

Weather report at PAO was 1500 ft. scattered clouds; but visually clear above airport and to west of airport. Could not visually see north east / east of airport due to buildings blocking view where aircraft was parked. Aircraft used G500 avionics instead of the six-pack that I am accustomed too. Additionally; I was trying to leave quickly and get to my intended destination. Furthermore; I have limited recent time at PAO (though my initial flight instruction was at PAO). PAO is a busy airport with non-normal operations. I was heads down dealing with unfamiliar avionics; dealing with the unfamiliar airport; and rushing to get in the air. Run-up area has us looking to the northwest / west; so the sky was still clear for that direction. Once I announced I was ready for departure; Tower quickly had me entering the runway and taking off; so I was focused on the initial take off operation rather than my surroundings. I took off on a right crosswind departure to the north-east and immediately noticed a thin layer of clouds that I might be able to climb above before encountering them; or turn back to my airport. At this time; I was handed off to NorCal for flight following. I decided to clear the clouds and started climbing at Vx (not Vy). I did switch to NorCal; but did not make announcements as I was focusing on aviating first; then navigating to ensure I did not head into the B airspace. I did not clear the cloud ceiling and was suddenly in IMC. I pulled back and triggered the stall alarm instinctively. While fighting my stall alarm instinct with my 'climb climb climb' instinct; I came to my senses and focused on flying at Vx. The avionics for heading were unfamiliar and so I could not use them and rather depending on electronic aid 'foreflight' to ensure my direction was between the class B shelf to the northwest and the class C airspace to the southeast. It was unclear whether I was under the 3000 ft. floor or 4000 ft. floor of Class B but it was my secondary concern (keeping plane level and climbing was primary concern). Suddenly I was over the clouds at around 3000 ft.; and therefore I focused on staying under the 4000 ft. shelf and above the clouds. I was able to confirm to myself I was outside the class B airspace and could maintain staying out of the airspace. The NorCal Operator did not want me to fly over 3000 ft. for flight separation with an aircraft entering OAK. They at first suggested I turn back; but I was concerned I would be flying back through the clouds and that it was better for me to continue towards my destination. He then suggested I could also make turns until the traffic was clear; and so I made tight turns between the airspaces and between the 3000 ft. cloud ceiling and 4000 ft. Class B floor. Once traffic was clear; I was able to proceed on my flight plan to ZZZ (about 4 hours away from PAO). Corrective Actions 1. I should have taken several minutes to familiarize myself with the flight avionics before leaving parking and heading for run-up. 2. I should have reviewed surrounding airport METAR3. I should assess the clouds in all areas and include contingency plans (takes a quick second)4. I should let the Tower know that I need to take a quick second to look in previously obscured areas before getting into the traffic flow5. As soon as I saw the layer; I should have requested to Tower to make right traffic and land to re-assess the weather and plan. 6. I should have felt more empowered to suggest to NorCal Control that for flight safety I needed to remain on my flight plan (or request a clear airport for landing). It appeared the hole over the airport was rapidly closing.7. In addition to mentally running through take-off abort actions; I should run through weather checks.