How can I obtain the current cart for a customer if my site does not require login?

I am developing a Shopify app that sets prices dynamically. When a user selects their inputs and the product(s) they want to buy, I want to use the storefront API to add this new item to the customer’s cart with a dynamic price.

However, from the documentation it appears that in order to obtain the existing cart (to see if they already have any items in their cart at the moment) I can only obtain that by specifying a username (email) / password for the current user.

Since we don’t anticipate requiring logins for our site, how can I determine / retrieve the current user’s cart? Is the only way for me to do this to track the cart id associated with the current session with my own custom logic?