B787 Captain reported an intermittent fumes event during pushback which was getting stronger. Shortly thereafter the Left Pack tripped off which prompted a return to gate for maintenance.

Narrative

Aircraft xxxx; 787; less than a month on property; had multiple previous write ups on problems with left pack and air cycle machine. In flight planning; I spoke with dispatch and Maintenance Control about my concerns with the write ups on the pack. Maintenance Control was not concerned. Throughout the cockpit setup; I would smell a burning smell but it would go away. Mechanic came in to do ETOPS check and the smell came back. I asked him if he smells it and he said yes but didn't know what it was. The smell dissipated again. Then during pushback; a strong acrid burning smell was coming into cockpit. No smoke just smell. I had push crew stop push. It was getting so strong that we considered putting our oxygen masks on but then it started to lighten up. I called FAs to see if they were smelling anything unusual and she said they were and it was really strong especially mid cabin. The FA at door 2L said that there was a very loud whining /grinding noise and the smell was getting stronger. At that point; we saw the EICAS message 'Pack L Off' and confirmed that the left pack had tripped. No smoke was ever seen in cabin. I asked ground to walk around aircraft to see if they saw any smoke around fuselage. They didn't notice anything unusual. FO contacted local maintenance to request return to gate. I called Dispatch to talk to Maintenance Control. Maintenance Control never answered so dispatcher just said he would get a gate for us to return to. We were unable to return to Gate XX because we were already north and there were airplanes behind us. Ramp was able to get Gate XY for us and after some coordinating with ramp and ground control; we were able to get into the gate. Maintenance supervisor and several other mechanics came into cockpit and instantly smelled the acrid smell. We briefed them on previous writes ups and they left to work on the problem. They worked for quite a while. We had the passengers deplane to wait in boarding area. Since it was a two person flight crew to ZZZZ; we timed out at midnight and flight was cancelled. There were no injuries or reported illness from the fumes.