If you miss the delegation deadline for the epoch that starts on October 1, the next epoch begins on November 1.
You will be able to submit delegation at any point in the month of October and validators will be able to accept it for the next epoch (again, it is recommended you submit no later than October 28).
Note that while you may be accepted prior to the start of a month, active staking will not take place until the beginning of the next epoch (November 1). The Proof of Use period in this instance will end 60 days after the start of staking which will be on January 1 at 12:00 AM UTC.
Similarly, If you miss the delegation deadline for the epoch that starts on November 1, the next epoch begins on December 1. You will be able to submit delegation at any point in the month of November in which case the same 60-day Proof of Use period will apply although in this case beginning December 1.