How do I create a add to shopping cart after they submit a form which already has different products/options in it?

Unfortunately, the form does not have a function that add products in a cart. You can add a payment integration and it will directly process the payment after the submit button is clicked.

However, if you have an ecommerce website with your own payment integration, then perhaps you can pass the submission data using POST method on your "Add to Cart" system or script. Here's a guide about it: https://www.jotform.com/help/213-Send-POST-Data-From-JotForm-Using-PHP-in-Custom-Thank-You-Page 

May we know what kind of platform you are using? Perhaps we can check it further.

The payment tool on the form itself acts as a shopping cart and the payments are processed directly from the form itself. It may be possible to send the products selected on the form to bigcommerce using its API or webhooks, but it seems that it is required to have a good knowledge in using bigcommerce API. You may need to hire a developer to achieve this requirement.

Hope this information helps!