DNA is actually visible. It is rather easy to compare ape DNA with human DNA for someone who understands DNA.
The invisible Biblical character known as "God" is very shy for an omnipotent being, and has made very few personal appearances. One would expect that he would resemble a human, being as he supposedly made man in his own image, but when he felt a need to speak to Moses, he preferred to take on the form of flaming shrubbery.
I do not think most people would be all that impressed to be discussing issues of morality with a flaming shrub. I would think that simply looking like George Burns or Morgan Freeman or perhaps James Earl Jones would be a more impressive choice. Or even a talking lion.