How can I go about bundling a worker.js into my plugin bundle index.js?

I am loading my plugin via script SINGLE script tag from the CDN, and I would like to set up the web worker once the plugin loads.

Can I bundle my web worker into the index.js bundle? I am using Vite to bundle the project.

It seems to be working fine when I run vite dev server but once I run the build it bundles it separately into the assets folder as well as serving it as HTML rather then js file.