Many thanks for your query; and no offence taken. You have posed a genuine question based on your true and faithful perception and understanding. We cannot knock that!
As you say, Sikhs are forbidden from engaging in "illogical" behaviors like fasting, penance, daily rituals, self-mortification, ceremonial marks, purifications, cleansing baths or pilgrimage; these are rituals which do not bring you closer to "God" or improve your moral well being.
However the logic that you use to seek proof of God is flawed. God is not a thing; it is not a spirit; it is not a slave of science. Science is not a explanation of everything; science is a study of the world that we see, feel, perceive and can somehow sense. However, there are some things which can only be perceived by the mind and soul and the study of this is called "Religion" or "theology" or "yoga", etc. Science has no perception of mind and soul and these are not recognised by modern science but these play an important part in religion.
If you meditate and train your higher mind functions, you will begin to perceive God. Just like once you train your mathematical and scientific skills you begin to understand the laws of gravity; of radiation; of nuclear physics, etc. In a similar manner, read Gurbani and you will being to understand the laws of Gurmat.
Let us just consider one historical incident from the life of Guru Nanak. You use science to explain the event while I will use Gurmat to justify the event. The event that I am thinking of is the sakhi of panja sahib. As you know, Wali Kandhari "pushed" a huge rock weighting may be a tonne or more down a steep hill. All these features - the hill, the rock, the Guru hand print, etc are still present in Hasan Abdal in Pakistan. You can go and do your science on these items of history. This huge rock with a huge amount of kinetic energy was "stopped" by the palm of Guru Nanak.
Now you have to explain how science can explain the ability of Guru Nanak who weighed less than 100kg to stop a rock travelling like a locomotive down a steep hill with his palm!
I would like to suggest that science cannot explain such an event! and that some other laws or other natural forces operate in such circumstances when such a person is involved.
You have to keep an open mind and read and observe these special events to see how at times the laws of nature can be enhanced under special circumstances.
I hope this helps you to find the answer to your question.