The phrase "that even exist" is correct and usable in written English.
You can use it to express surprise or excitement over the existence of something, usually following an introduction of the thing. For example, "I had no idea there was a program like this that even exist!".
Moreover, the issues of slim margins on ads that even exist for large, world-famous publications are only compounded for smaller ones: they have a hard time getting the economies of scale needed to make the ad-based model work.
How… does that even exist?
The home of Don's Carousel pitch, the place where you know you are loved… does that even exist anymore for Don Draper?
Once he entered University of Indiana to study organ at a higher niveau, Taylor found an even larger punk-led community of his fellow "freaks": "I started hanging out with them — we all partied together — and so I became part of a counter-culture — well, not 'counter-culture'... does that even exist anymore?—that was largely populated by queer kids.
Once he entered University of Indiana to study organ at a higher niveau, Taylor found an even larger punk-led community of his fellow "freaks": "I started hanging out with them and we all partied together and so that because part of the counter-culture— well, not 'counter-culture'... does that even exist anymore?—that we inhabited that was largely populated by queer kids.
I didn't know that even existed.
Not everyone has someone to show them right off the bat where the underground is, if that even exists anymore.
I think Google forgot that even existed, as it's sometimes prone to do.
"Even though that's something that cannot even exist".
How does that thing even exist?
"Does that person even exist?" asks Sanderson.
