My quick read of the posts reveals only 2 that come close to a sound Torahic answer: Charliehall, who notes that HaShem’s existence is a principal of faith, which some of us recite every morning. This is consistent with Rambam, who authored the 13 principles of faith. frumnotyeshivish gave a good answer by referring to a book by Rabbi Keleman, “Permission to Believe.” Neither of these answers is really one sentence, but never mind that.
Many answers attempt to bend Torah into a quasi-scientific notion. That is utterly unsound and disrespectful of the Torah. HaShem does not need rational proof and does not want us to pursue rational proof of His existence. He wants our faith.
All the proof we need is in the Shemah.