It's one player's first session of the campaign. While walking through the woods he encounters an NPC cutting down a tree with his son. While chatting, the young boy says "Hey dad! Look what I found!" and he is holding a baby owlbear. Not long after that the mama shows up in a frenzy.

One possibility is that the owlbear attacks the boy, reducing his HP to zero. Then the owlbear grabs the boy by the head and runs off to it's lair. This would create a second encounter in the owlbear's lair, in which he has advantage.

Anything to add?

I've found that my players always sympathize with Owlbears... I think they're generally treated as just animals despite being categorized as Monstrosities.

That said, my thought process is I think you could do something fun where the Owlbear mistakes the little boy for her child. Like... maybe the kid is wearing a feathery outfit, like maybe the town he's from hunts Owlbears semi-regularly, so it's not unusual for him to be wearing an owlbear-skin coat. So the Owlbear goes to rescue her child, but by the time she gets there this kid has the scent on him of the Owlbear cub. So by the time the party catches up she's trying to feed the kid which, y'know... would be a terrible thing to live through, assuming she feeds her kids in the same way an owl feeds its children.

Wouldn't the owlbear just grab her/his kid, the cub/fledgling?  Why would it bring the NPC humanoid child to its lair if its trying to prevent these humanoid types from getting close to its own kid?  I know that an Owlbear is technically a Monstrosity, but if it has anywhere near a natural bear's intelligence, it would NOT want the creatures it just attacked to know where its lair is. I suggest you either have the plahyer's PC show up just in time to possibly prevent the Owlbear from doing fatal damage to the humanoid father and son if you want the possibility of not having an automatic dead Owlbear or dead humanoid at the end of the whole encounter.  Or have the PC encounter the Owlbear in some other situation. 

For instance, you could have a scene where two semi-adult Owlbears (slightly reduced HP) are rough-housing the way adolescent predators often do. Nearby is an object that looks possibly valuable to the PC or to someone the PC wants to help.  Now you have a situation where the player needs to think about whether to fight, scare off, or stealth around the Owlbears.  

Third option, you announce the entrance of momma owlbear onto the scene, and describe her enraged bellows as she frame out about her poor baby in the hands of those meanmean humans. The kid drops the wee baby owlbear and runs to his da for safety, then you declare “roll initiative” and make the encounter all about chasing the owlbear off and protecting the woodsman & son. Remember, most animals will only fight to the death if they have to, so once the cub is safe momma owlbear will likely run off with it once she’s reduced to ½HP. That’s a victory situation for the party. The second encounter is after the woodsman and his son are safe and well on their way home that poppa owlbear shows up to finish what momma started. It’ll also run off if reduced to ½HP, but combined that’s a whole owlbear the party defeated with a brief timeout to heal up halfway through if necessary.