When infinity is applied to space, you have omnipresence. God is omnipresent in that He is exalted above every limitation of space. The limitations of space are distance, size and form, and the fact that a body can be in only one place at a given time. When the child of God hears that His Redeemer-God is everywhere present, he is certainly filled with awe and amazement. When Solomon dedicated the temple in Jerusalem to the true worship of God, this king would have the people of Israel know what kind of a God they were to worship there.
Space is a creature, just as time is.
And we need space just as we need time. God does not need space, is not affected by space, and does not think in terms of space. God's omnipresence is that virtue according to which He is present in every point in space with the whole of His Being. Now we are apt to think that God fills the entire universe which He created, and then goes a little bit further than the edges of the universe. But God cannot be contained by space.