Seasonal jobs that might turn permanent (Pittsburgh)

A staffing agency says some roles convert to permanent after 9 weeks. This is my first time dealing with any of this. I would like to avoid a gap in my résumé. Has anyone been converted to permanent?

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

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