The WooCommerce support staff can maybe suggest a product carousel extension. “Extension” is their term for another plugin. If you’re keen to avoid another plugin, you could develop your own solution, but it’d likely be implemented as a plugin anyway. The main difference being it’d be your own plugin, not from someone else. You can keep all of your custom code in a single plugin.
A carousel involves two basic parts. The HTML content for the entire carousel, and JavaScript to manage the carousel display. To generate the HTML content, you’d need to alter the page’s template or use an existing action hook to inject additional content. If you need help doing this, WooCommerce support is your best resource.
While it’s feasible to develop your own JavaScript solution to run the carousel display, you’d save a lot of time by utilizing an existing JS or jQuery library to do the heavy lifting. Your custom script would merely instantiate the library using certain parameters to fine tune its behavior to work with your HTML content.
This can be rather time consuming unless you’re an experienced developer. You’d save a lot of time and effort by using an existing plugin.
