The idea that the Ka'ba is the "House of God" is metaphorical. It is called the "House of God" because it is an ancient center of worship and a sacred land with special spiritual characteristics that people can physically go to to have a stronger sense of God or the spiritual world. Also, according to narrations, angels frequently visit it.
However, according to mainstream Islamic belief, God does not exist in any physical place or time. This is because the universe is created, and God is not material or confined by space or time. God is aware of everything in the universe and in control of it but not actually in it. (That is, a refutation of pantheism)
Some might say that the universe is a manifestation of God or Gods' attributes, or that material creation is dependent on God for its continued existence, but God is not actually inhabiting the universe. Indeed, in the Qur'an, God introduces the possibility of multiple universes (since "God of all the worlds" can also mean "God of all the universes") and speaks of the creation and destruction of the universe. Of course, sometimes mystics and others have their own ideas about the nature of the divine.