I was recently asked if humanists have an open mind about the existence of god, and what science can do to find god. My opinion is that the answer is yes, but that humanists haven't seen anything that they would consider evidence of the existence of an anthropomorphic god. Scientific research into the existence of god really doesn't have any good place to start. The existence of god will need god to provide an unambiguous signature of his presence. Measuring wavelengths, timing events, creating compounds are the kinds of things scientists do, and do very well. Those things aren't like to produce the answer to life, the universe, and everything any time soon.
In myth and legend gods interact with humans all the time. But generally only in private so you have to take the word of the person who suffered the divine presence. "You saw who? And he said what? And he personally gave you that magic kazoo that can heal the sick. Oh, but you can't cure my athlete's foot right now. Uh Huh." God needs to be less shy to overcome natural skepticism in a scientific age.
There is a common argument that god shouldn't provide proof of existence because that would rob man of freedom of choice. That man must prove his allegiance through faith rather than evidence. I find that argument less than compelling. First, of course, there is the inherent unfairness of god taking that precious gift away from so many of his messengers. Moses, anybody who got healed by Jesus, Joseph Smith, or anybody else who became a prophet of god through divine communication just got screwed. Hardly the actions of a just god deserving of worship. Second, and more important, just because you KNOW god exists doesn't mean that you will choose god. Plenty of people choose to be evil. Just ask Judas or Lucifer. Freedom of choice is still there, it is just a more informed decision after god gets a regular talk show on Fox News. (The other networks probably wouldn't give him a show.)