That bag probably has enough air volume to last someone around 5 minutes (give or take, probably give since that's based on adult respiratory rates, and that's a kid) before noticeable symptoms of hypercapnia (too much CO2, which will become a problem before oxygen deprivation does) start setting in.

Depending on how wide the river is, that's not actually too much of an issue.

I mean, it’s possible he’s gripping a pipe/snorkel of some kind in his hand protruding through the top of the bag itself.

He’d just have to grip it tight and hold it above water as he wades through. Perhaps it’s just deep enough that there’s not a reasonable way for him to hold the kid completely out of the water, but it’s easy enough for him to hold him up just enough that water doesn’t come in over the top of the bag itself.

With the amount of air in the bag to be “full” and relatively pressurized, he’d reliably have several minutes before any issues. It’s not like it’s suctioned around the kid’s face. There’s several minutes of air in there. More than enough time to ford a river with width measured in yards.

Besides what others have suggested, there might be areas of the river shallow enough for him to pause, both to rest and to refresh the air supply.