I’m afraid a lot of folks are misinformed on this topic. There is no “Domain Age” factor that I have ever seen. There is an “indexed age” factor but not a domain age factor.
The reason an SEO agent may look at “domain age” is because it is relatively easy to look up, while age in the index is not as easily ascertained, especially on bulk research. Naturally, for a page to have been indexed for a long time it would have to be on a domain that has been around for at least the same amount of time. So “domain age” is only meant as a method to filter out new websites that couldn’t possibly have “indexed aged” pages. Domain age is not a ranking factor, but just a hint to researchers that the website may have been around a long time, and may have aged pages within the search engine indexes.
The idea that you can purchase an aged domain and benefit from the age of the domain is invalid. You can, however, purchase a domain that has “aged backlinks” pointing toward pages on that website. By placing new pages on the same URL that those “aged” backlinks point toward, you benefit from the link juice being passed by those “aged backlinks”.