Custom signup form with API V3

Hello,

I'm trying to add contacts via a custom form (not a standard CC form) on a website, but don't want the user to have to take any other actions other than submitting the form. Is this possible?

I'm able to add a contact using the server flow, but only after I've logged in and that won't work for anonymous users visiting the website that want to just sign up.

I need to use a custom form because I'm doing things on my end with a database that stores data being used in a CC custom field that gets sent along with the contact information when the contact is created.

All I've found is outdated methods that don't work.

Thank you