A321-NEO Captain reported returning safely to LAX after experiencing pressurization issues. During the return the flight encountered wake turbulence from a preceding B737.

Narrative

Mechanics were working on the airplane when we arrived at the gate. An MEL was created: 21-XX Skin Air Outlet Valve (MMEL 21-XX-XX) and signed off. We were about to push back and the avionics door reopened. Captain and I went outside multiple times to check on status and mechanic was back in the avionics compartment. Once done; after maybe 20 minutes the mechanic came up to the flight to apologize and said that his colleague forgot to bag the loose connections but that now everything was done and in order. Both the captain and I at that point decided to depart as everything was in order. All doors were closed. Everything went normally until the takeoff. During the TO roll an ECAM message appeared and we decided to continue as it seemed related to the MEL. After takeoff more ECAM messages appeared mentioning that the max altitude was 10000 ft. We weren't pressurizing at that point and decided to level off at 10000 ft. We advised ATC. Went into a hold. Ran all checklists. We decided to burn fuel in order to be below max landing weight. We did [request priority handling]. Once max landing weight was reached we went back to LAX for ILS25L. We got into the wake turbulence of a 737 at about 3000 ft and had to turn the autopilot off to recover. Then the landing and taxi to gate was normal. No assistance needed from safety vehicles. Cause: Maintenance might have made a mistake following that MEL causing the aircraft not to pressurize. Extra attention should be given to MELs.