How long does it take for a waiver to connect to Square?

Also how long does it take for a waiver to connect to square? We’d like to connect our new customers to their purchases immediately when they come in.

Normally, once the user fill-up the form and submitted it, the payment will be processed instantly by the payment gateway as well.

I checked your form and I can see that it is already connected with Square. However, the payment section is empty, there are no products available. 

Here's a helpful guide: Setting-Up-Your-First-Order-Form

I also suggest you check these guides as well:

Order-Form-Basics
Order-Form-Types

If you don't want to set up products and you want the user to define the amount that he/she will pay, then please change the Payment Type to "User Defined Amounts" or "Collect Donations".

Hope that helps. If this is not what you need, let us know so that we can further assist you.