They couldn't do that because a Go board has 19x19 intersections, each of which can be either blank, or have a white or black stone on it. This gives a grand total of 3^361 possible configurations before we consider the actual configurations that are legal, which is "only" about 2*10^170.
It's impossible to convey just how stupendously enormous that number is. It's far, far bigger than the number of elementary particles in the universe. Actually, if every elementary particle in the universe held its own universe inside it somehow, then the total number of nested particles would still be great way off from this number.
So no, Google definitely does not have the resources at hand. God himself doesn't have the resources at hand. Of all the ways you could have a computer "solve" the game of Go, this one is definitely, capital-I impossible.