Hi @ZubirIsmail, to "index" a Looker Studio report in Google search, you essentially need to embed it on a webpage that is properly indexed by Google. This means publishing your Looker Studio report to a website and ensuring that the webpage that contains the embedded report is accessible to Google's crawlers by following standard SEO practices, including submitting the URL to Google Search Console to request indexing.
I linked to some resources in this comment for you - and I also found this video about how to index a page that I hope will be helpful.
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