Why is that proof for God's existence is something that people continue to attempt regardless of it being impossible and why is it impossible?

Proof of Jehovah God's existence is all around us, specifically in nature. (Romans 1:20) Everything in creation didn't just appear out of thin air; it had a beginning. The of something being around since forever is difficult to comprehend, but that doesn't make it impossible.

It's been said that energy can never be destroyed and has been around for eternity. So it would make sense that a being with access to said energy (as well as being responsible for the energy in the first place) could also be around for an eternity. Considering how much energy exists in the known universe and how much exists, in order for someone to have created it they would need to have more power, longevity, and intelligence than anything in existence. In the very least, this would make this individual god-like. It would also make sense that this being would deify themselves in the eyes of their creation (a.k.a. make themselves God). In addition, it would make sense for Him to leave a record of His dealings with mankind throughout history, as well as their purpose, where they were headed as a species and how He wishes for us to conduct ourselves. This record would withstand the test of time as well as anyone that would try to tamper with and destroy it. (a.k.a. The Bible) Being an entity from a higher plane of existence, it would also be logical for Him to be able to communicate with His creation through other means than what we consider normal. (a.k.a. prayer)

(New World Translation of the Holy Scriptures)