Hello Will,
Thank you for reaching out about the issue with your sitemap.xml file not being indexed on Google.
The common reason why your sitemap.xml file is set to no-index is that the pages or posts are set as "Noindex" in the Robots Meta tag settings. This setting excludes them from the sitemap generated by Rank Math, resulting in a 404 error.
To fix this issue, you need to ensure that your posts and pages are set to "Index" in the Robots Meta tag. You can check and change this setting by navigating to Rank Math SEO → Advanced tab in the post editing screen. Here, make sure the Robots Meta tag is set to "Index" as shown in the screenshot below:

After updating the settings to "Index," remember to save the changes by clicking the Update or Publish button.
If after making these changes, the problem persists, you can also check for any unintended rules in the robots.txt file or conflicts with plugins. Additionally, you can exclude the sitemap files from caching in your caching plugin to ensure they reflect the latest posts and URLs of your website.
I hope this helps resolve the issue with your sitemap not being indexed on Google. If you have any further questions or need assistance, please feel free to reach out to our support team for further guidance.
Best regards.
Sources:
Why the Sitemap_Index.xml is Throwing a 404 Error » Rank Math
Rank Math Sitemap Issues and Their Fixes » Rank Math
Why Isn’t My URL Included in the Sitemap? » Rank Math
Hello,
Thank you for contacting us and bringing your concern to our attention.
Please note that by default, sitemaps are set to Noindex as they are meant to be crawled and not to be displayed on search results pages and it is absolutely fine.
You should only submit your sitemap to the sitemap section of your GSC account and shouldn’t use the URL inspection tool for the sitemap URLs.
https://rankmath.com/kb/submit-sitemap-to-google/
Hope that helps and please don’t hesitate to let us know if you have any other questions.
Thank you.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.