I had always assumed that Hunter-Gatherer societies were very loosely sex divided and strongly necessity based. Meaning, sure men could be the typical hunter and women the typical gatherer but if necessity dictates, any person would do any job, and, given the times, that was probably frequently.
Furthermore they also likely didn't have societal structures the way modern societies did, meaning people likely weren't barred from any job or forced into any job, it was a community effort for survival, if you meet a criteria that can help, you do that.
These are not factual statements, these are just my assumptions on how I figured they reasonably existed.