Seasonal jobs that might turn permanent - 4 weeks in

A staffing agency says some roles convert to permanent after 10 weeks. Any experience at all would help. I would like to avoid a gap in my résumé. Which employers treat seasonal workers well?

Keep a list of supervisors' names. A reference from one of them helped me land my next job.

I was converted after one season because I showed up every day and volunteered for extra shifts. Managers remember that.