Seasonal jobs that might turn permanent - 21 weeks in

A staffing agency says some roles convert to permanent after 6 weeks. I have read a lot of threads here and could not find my exact situation. I would like to avoid a gap in my résumé.

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

Apply to several. Start dates and schedules change quickly and having options helps.