Seasonal jobs that might turn permanent - what worked for you?

A staffing agency says some roles convert to permanent after 9 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. Has anyone been converted to permanent?

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

Ask early about permanent openings. Some teams fill them from their seasonal list.