Seasonal jobs that might turn permanent - first time posting

I am looking at seasonal jobs around St. Louis that might lead to something longer. I do not usually post, so bear with me. I would like to avoid a gap in my résumé. Has anyone been converted to permanent?

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.