No, Google knows very well about each and every older source, it just refuses to show them.

Here, I can easily prove it: search for something like "site:theguardian.com" and set the date filter to show you results before say 1/1/2020. I guarantee you you won't find a single news article within search results. You will find other pages from their site such as tag pages or old job postings of theirs and what not, but no news article what so ever. Then swap The Guardian for whichever news source you want and do the same.

Then do the same on say DuckDuckGo and it'll work as intended.