Maintain cart on all pages of other web site

We’re adding Buy Buttons to half a dozen products on our non-Shopify web site. When a product is added to a cart, we’d like to maintain the cart object (icon) across all pages of the site including those without a Buy Button. Is there a script snippet that can be added to a global header to accomplish this?

Are you able to use the JS buy SDK instead?
https://shopify.dev/custom-storefronts/tools/js-buy

Thanks Jason. Our plans are to use our existing site for a short time then sometime early next year roll over to the Shopify hosted site. As this is just a gap measure, I was hoping I could simply add a cart script to the global header but if that doesn’t exist then I’ll check out the SDK.