There are some articles out there that say your web page needs to be ranking in the top 20 results (either on page 1 or 2) in order for Google to display the content as structured data. This is not true at all.
Generally speaking Google will only display structured markup on page one of its SERPs for some of it's data types like FAQPage for example. But if you implement star ratings, these will display on whatever page in the SERPs you rank for.