In this case, of course God cannot be required to submit to examination under a microscope (or telescope) because He is the Creator of the physical Universe, and hence outside of its laws; in fact, He pervades and yet exceeds the Universe He made, and is outside of time and space.
However, He does reveal himself.
We can know something about His character by His works of art, just as we can know something about Shakespeare or Van Gogh or Michelangelo from the whole body of their works. In addition to this natural revelation, there is also supernatural revelation: the Holy Spirit spoke through the prophets, through the words they spoke, through their recorded words, and through the Church, which is the guaranted interpreter of Scripture.
"Upon this Rock I will build my Church, and the gates of hell shall not prevail against it."
Such is the evidence.
I realize that not everybody accepts it, but that could not be because there is too little evidence, but rather too much for us to compass, since it includes the entire Cosmos. And more.
We were talking about evidence of free will, not the existence of God.