God either exists or he does not. It's as simple as that.
There is no scientific proof that God exists and no scientific proof either that he does not exist. I specifically use the words “scientific proof” because you are using the adoption of science (read nuclear propulsion) by humans as as proof of the existence of God. Depending on your geographical position on earth or religious group you were brought up in, you and the next person may probably not even agree on who God is.
You may be referring to the Christian God, and an inhabitant of the island Tannu in Vanuatu, may be referring to John Frum. If you are interested in comparative religion you will find reading up on John Frum fascinating.
The Merriam-Webster Dictionary defines proof as "the cogency of evidence that compels acceptance by the mind of a truth or a fact". Neither believers nor non-believers can supply any cogency of evidence that will compel acceptance by the other side.
I believe that trying to convince the other side in believing, or not, in God or any other creator by scientific proof is fruitless. People will believe what they want and it is their good right to do so.
However, it you feel you must try and convince someone, it is your duty to try to the best of your abilities to provide a watertight argument.
I lost interest in your "letter of proof" as soon as I read the line that a dolphin cannot play the violin. You infer that humans are "special" because they have a high level of self-awareness and comprehension, and that that fact, in some way acts as proof that God exist. Your mistake lies in selecting an obvious human ability as a measurement for proof that God exists.
Let's change the "ability" to match a different species in order to prove that God exists. You will see that your argument is patently absurd and the fact that other species is specialised in other abilities, their mere existence “proves” that God exists.
Deep diving – sperm whales can dive up to 3 km’s deep and stay submerged for 90 mins. We humans cannot do that. Therefore they are more “special” than humans and that proves that God exists.
Limb regeneration – Salamanders can shed their tails to distract a predator and then a new tail grows in the place of the old one. We humans cannot re-grow a lost limb therefore salamanders are more “special”, and that proves that God exists.
You see? Your argument proves nothing except that the parameters you chose to try and prove the existence of God, was flawed. Your argument jumps between attempting to prove the existence of God by science, reasoning and thought experiments. None of which supplied any cogency of evidence that will compel acceptance.
I therefore cannot accept the “proof” that you supplied.
On a more personal note, I am of the opinion that the fact that you need to prove His existence, means that you have had your doubts about it yourself. Incidentally, I also believe that is how a lot of Atheists are born.