I saw an analysis by a meteorologist on Twitter that used a NOAA wind model and the publicly known position of the balloon (when it was above Montana) to backtrack a likely path, which ended up with an origin in China:

https://twitter.com/wildweatherdan/status/162132105562836582...

The same person posted a similar analysis of an object shot down over Alaska that suggested it could have been a National Weather Service balloon: (or trying hard to pretend to be one)

https://twitter.com/wildweatherdan/status/162416175081471182...