USCIS has now officially stated that H-1B cap-subject petition may have a start date of October 1 or later (and six months or less from the receipt date of the petition). Previously, USCIS required that the start date be only October 1.
In FY 2021, USCIS rejected H-1B filings for stating a start date that is after October 1. Lawsuits were filed and USCIS lost. Those rejected were given the opportunity to re-file. As of August 30, 2021, USCIS has updated its own web pages to acknowledge that H-1B cap-subject petition may have a start date that is after October 1.
Related post: Some H-1B Petitions (Cap Subject) were Rejected Last Year Because the Petitions Included a Start Date After October 1