in reality, not in a story. in a story it is always much more improbable
Not really. Across all the games you've played, how many times has the main character met someone new? Because that's all we're getting here, and she might not even be new to the MC, she's just new to us. Let's make up some random scenarios though that would lead to the MC and his child being in the jungle with a woman we don't know, and they're all dirty:
1. They're taking a tour and the bus goes off the road, the passengers have to get out of the overturned vehicle and hike their way back to civilisation.
2. MC, his kid, and his friend who he has known for a few years (bearing in mind this is a few years in the future if that's his and Jaye's kid) were exploring or playing and got filthy, they're walking back to wash and have dinner.
3. They're on a family holiday and there's a hurricane, MC is carrying his kid to safety while the woman who was in the room next to them walks alongside him.
4. Jaye died in childbirth, MC and his new wife take the kid on their honeymoon but they get lost on a walk through the jungle.
5. MC is doing humanitarian work, the kid has been helping and now they are heading back to base with one of MC's co-workers.
I took almost no time to think of those examples, and it would have been a hell of a lot easier if they weren't covered in dirt in the render too! It should be noted that none of the examples require Jaye to be in the render as well in order for them to be believable. She could be walking ahead (or behind) or she could be somewhere else entirely - it's not outside of the realms of fiction for Mum to be elsewhere while Dad is with the kid.