I tend to sneak around, steal the egg unseen and run out again. I never, ever, ever fight the Owlbear. Not since EA when I learned you can recruit the cub. There is NO way in Avernus that I play this game without the Owlbear Cub.
On my very fist Honour Run, I did pretty much everything possible in Act one besides the Creche, and only then went on to deal with the Goblin Camp. I accidentally nuked the Cub with Barcus' Heavy Backpack and restarted right there and then.