Share 'how soon is too soon? re:apps for autumn/winter'

How soon would you say is too soon regarding applying for work starting in late October/early November? I am hoping to get a retail supervisor position. I have 20+ years experience in retail and received (unofficial) supervisor training on the job at GCSR. I will be at GTLC until early October and would like to have something lined up quickly within 3 weeks of my end date.