Checkout these points:
- Favicon Guidelines: Google has specific guidelines for favicons. Your favicon must be a multiple of 48px square (for example: 48x48px, 96x96px, 144x144px, etc.), and the favicon URL must be stable (don’t change the URL frequently).
- Crawling and Indexing: Google looks for and updates your favicon whenever it crawls your home page. If you’ve made changes to your favicon and want to inform Google about the changes, you can request indexing of your site’s home page. It’s also important to note that the favicon file must be crawlable by Googlebot-Image and the home page by Googlebot; they cannot be blocked for crawling.
- Time: Having your favicon displayed by Google takes time. It can easily take more than a week, even if your site is reasonably popular.
- Technical Issues: Ensure that your favicon file is not a 0 byte resource. Google might try to use it since loading /favicon.ico is a well-known convention.