I never said that it should be convincing to everyone, but "good evidence" requires inter-subjective agreement and peer-review.
The philosophy of science has limitations. It does not work for all possible phenomena that an objective observer can observe. For example, we have all had dreams to know dreams are a common phenomena of the brain. This can be proven with the scientific method through common experiences of the basic dream schema.
However, the details of any specific dream cannot be group verified, by the scientific method, since there are no tools that allow others to monitor your dreams in the third person. Others cannot recreate a very specific dream to determine if all the dream details, actually occurred as specified. How would you peer review dream details without having faith in the person telling the dream? Even if the dream and the person were both objective and valid, it would be called subjective, due to being proof by one, beyond others to verify?
The philosophy of science limited itself to only those things that come into the brain, from the outside from our sensory systems. Tools help to extend this range. It is not as well designed for all those other objective things that consciousness can perceive from the inside. This is the last frontier of science.
Math Proof for God
Science often uses math proof along with physical evidence. For example, nobody has ever gotten up close to a black hole to gather hard evidence. What we know is based on some circumstantial evidence from far away, theory and math. There is some faith involved. Using this same method of semi-math proof, there is a way to infer some of the classic parameters of God.
We live in what is called space-time. The concept of space-time is based on time and space being and acting interconnected. This is modeled with math. This connection between space and time places physical limits on what it possible in physical realty. For example, the fastest that material things can move in space-time is the speed of light.
Say mathematically, we broke down the math variable called space-time, into separated space and separated time, so space and time were no longer mathematically interconnected and dependent on each other. Now they are separate variables for different math. Theoretically, one could now move in space without the constraint of time, and/or move in time without the constraint of space, since the bond is broken.
If one could move in space without the constraint of time, this would allow one to be anywhere and everywhere in the universe at the same time, since space is not connected or dependent on time. This is classically called omnipresence. This feature of God dates way back.
If you could move in time without the constraint of space and if you were observant, you would know both the real time state and history of the entire universe, simultaneously. This is classically called omniscience. It appears religions deal with the math of separated space and time more than the math of space-time.
The simple on-off or binary switch between space-time being connected or not connected, breaks down the universe into two very different and separated realms. This is also a classic claim for the different living spaces for the humans and the Gods.
As far as physical proof that such a state actually exists, where space and time are not exactly connected, as space-time, science theorizes worm holes which are product of theory and math. These move material across the universe faster than a beam of light; warp drive.
There are also quantum affects that can depart from classic space-time. When an atom gives off a photon of energy, we have an affect that goes from inertial speed, to the speed light, in zero time.
Even the inflation period of the early Big Bang Universe can be explained as a special case, where space and time were not yet connected, as space-time, so moving faster than the speed of light was not a problem, even for the whole universe. Once space-time connects things changed.
The most interesting observation of the concept of disconnected space and time is connected to the human imagination. The imagination allows us to think outside the limitations of space-time; science fiction. I can imagine building a ten kilometer long bridge out of wet noodles. This will not work in space-time, due to the imposed limitations on matter and forces. But it is possible to imagine this, since space-time does not place limits on how information arranges itself in the imagination. The matter of the frontal lobe is connected to space-time, but space-time does not place the same limits on how the data can organize.
Innovation, for example, is often ahead of its time; iPad. A concept can appear in the imagination and then the drawing board, standing outside the limitations of space-time, until two realms meet in space-time; product launch. Consciousness appears to bridge the gap and gets information from both disconnected space and time and space-time; visionary and pragmatic.