I got stuck in at the beginning of Lambda Core in the garage area. I opened the closed double doors and the tank’s turret started turning to face me so I pulled out the rocket launcher and destroyed it.
After killing the remaining aliens and soldiers I wandered around trying to figure out where to go next for about 15 mins or so before figuring something probably didn’t go as scripted and so I reloaded an auto-save.
This time I waited and didn’t open the doors right away and let the battle inside the garage play out a little and the tank blew open the doors like it should have.
TL;DR: I blew up the tank in Lambda Core before it destroyed the doors and I was unable to proceed.