Is there a way to create a form that saves progress?

By default, Jotform has an auto save feature that automatically saves any changes you made on your form.

Also, all successful submissions are saved under your account. Here's how to view it.
https://www.jotform.com/help/269-How-to-View-Form-Submissions

If that's not what you meant, then please let us know and provide us more information on your query.