You can add all required libraries directly on your store, by editing your theme.liquid file and adding the CDN links between the <!-- Algolia head --> ... <!-- /Algolia head --> block.
Then you need to add them on the algolia_externals.js file. There is a guidance about this kind of implementation for both previous and latest versions of our extension documented here.
*Please note that as of January 1, 2024, Shopify no longer supports theme injections from the Algolia Shopify integration.