Can I Use Square for my particular payment gateway?

Hi. I have used Jotform for a number of years using Stripe to collect the payments. I have several hundred teams submit applications to participate in an event. They were required to provide credit card information. Only teams that were selected were required to pay - meaning after teams were selected, I would go back and charge just those credit cards. This worked really well with Stripe.

Do you know if I can accomplish the same thing using Square?

As far as I understood, you are mentioning about payment authorization. 
Guide: How-to-Enable-Payment-Authorization
This feature is also available with Square payment gateway. 

Thanks Alan. Unfortunately, the 6-day window is the deal breaker. In most cases, I would need a month or so.

Unfortunately, this is a limitation on Square end. Maybe you could collect users basic information and send them payment forms upon approval?