Phase devices are very much your friend, and they're not that rare a spawn; between them and invuln/zerk, your odds of surviving that initial ambush are actually not terrible.
Outside of that? I'm sure it's possible, but I have no idea how. Maybe I've been unusually lucky, but I've found that phases and powerups have made the Bruiser's respawns the real challenge of the Anomoly.
EDIT: I suppose that, if worst comes to worst, you can grab the two large health globes pre-ambush and try to overheal-tank your way to cover.