I will grant that initiation fees are legal in some jurisdictions, as are early closing fees. (money.stackexchange.com)
Many organisations accept applications all year round, but it's always worth checking individual employers — a few do specify early closing dates or advise early applications. (targetjobs.co.uk)
** Early Closed Account Fee — Fee assessed if account closed within 90 days of being established or if account is closed due to failure to return account opening documentation. (bayerhfcu.com)