Firstly it would help us help you if you provided a link to the website.
Yes with CSS.
You need to get the podcast icon as an image file, which is a slightly different thing as some icons are not image formats, you want a jpg or gif or even a png format and named file. Upload this image file to your website, say in “wp-contents/uploads”
Then you use your browser inspector to find the thumbnail and get a set of CSS classes and or id components that are specific to thumbnail, then (in the customizer “additional css” or child theme) add CSS so that the image file is a background image to the thumbnail, you may need to position and no-repeat it, possibly size it too.
If this does not work, then you could use a filter to introduce an img html element to the thumbnail menu item. Would probably also need css as well.
