Domain not ranking in Google until you reconfirm query

[imbckagn]

Say you perform a search for randomurl.com and the website doesn't show up in the search results BUT it says:

"Showing results for random url"
"Search instead for randomurl.com"

At this point "Search instead for randomurl.com" is a clickable link which places randomurl.com in the first search result what does this mean for randomurl.com?

Does it mean the website is in some sort of supplemental index or maybe it doesn't hold enough authority? I have seen many websites that this happens to and I would say 9/10 are very thin and fairly new. Content is always unique but not the best quality. Will randomurl.com ever be able to work it's way out of this?

[dipper]

new probably means the site isn't indexed .. try "fetch as Google" using Google Search Console, and then submitting the website to Google's index using the option.

[imbckagn]

I should have been more clear about the use of the word "new". These sites are anywhere from 3 months to 1yr old and they are indexed. The websites show up in the index when you click the "Search instead for randomurl.com" link. They also appear in the index when using any of the site operator commands. It almost seems like some sort of quality filter or sandbox.