I think you need to better define 'game' and 'made', probebly 'best' as well.
I don't think "impossible" is the correct term to describe answering the question as stands, I think "idiotic" is more realistic. I mean no offence, but that is such an opinionated question, that I do not think it should ever be asked by anybody. And anybody who would straight up answer it without the disclaimer of "I think" is probebly somebody who gives their own opinion more value than they should.
Maybe "what do *YOU* think is the best game?" or "What is your favorite game", but never "what is the best game?" Answers to those 1st two questions are easy to make. I'll even accept "what game does XXX the best?" since that is specific enough that it can be approched from a scholarly and factual point of view. I give give plenty of reasons why I think certain games are among the best games ever made. However I would never ever say they 'ARE the best games ever made' because I'm not that arrogant to think my opinion is 100% correct.
( no countering with Niche 'superman' arguements. I'll accept that if Niche is correct, his 'superman' might have an opinion worth using to dictate 'the best video game' but I doubt he'd be wasting his time with such questions anyway)
(btw, I'm in a bad mood, and I'm aware that I sound very nasty in the above paragraphs. Sorry to any who I might offend, please don't take anything I say personally)