From the State Dept. of Education, Child Nutrition:  

If a parent/guardian completed a free or reduced-price meal application in July or August 2022 and that meal application is approved for free or reduced-price meals, they will be eligible for Summer 2022 P-EBT benefits retroactively when pick-up files are sent to DHS in October. This will only apply to Summer 2022 benefits. If there are any questions regarding this information, please reach out to SDE Child Nutrition at 405-521-3327.