What, then, is there incredible in His manifesting Himself through that in which He is? By His own power He enters completely into each and all, and orders them throughout ungrudgingly; and, had He so willed, He could have revealed Himself and His Father by means of sun or moon or sky or earth or fire or water. Had He done so, no one could rightly have accused Him of acting unbecomingly, for He sustains in one whole all things at once, being present and invisibly revealed not only in the whole, but also in each particular part. This being so, and since, moreover, He has willed to reveal Himself through men, who are part of the whole, there can be nothing ridiculous in His using a human body to manifest the truth and knowledge of the Father. Does not the mind of man pervade his entire being, and yet find expression through one part only, namely the tongue? Does anybody say on that account that Mind has degraded itself? Of course not. Very well, then, no more is it degrading for the Word, Who pervades all things, to have appeared in a human body. For, as I said before, if it were unfitting for Him thus to indwell the part, it would be equally so for Him to exist within the whole.(Athanasius, On the Incarnation, Chapter 7.)
This is a rather striking argument. Rather than appealing to God's omnipotence and the paradox of the incarnation, Athanasius argues that God is already in everything, so why not a human being? This is not the only argument he makes, of course, but it seems significant that he makes it. It's hard not to see it as a theological misstep, since it would apparently negate the uniqueness of the incarnation as an incomprehensible mystery. If God is manifest in Christ in the way that the mind of a man is manifest in his tongue, then Christ would appear to be just a part of a big whole which God fills.
Then again, it isn't hard to find biblical evidence to support the idea that God fills all things. It just happens to get very confusing when you try to talk about incarnation as a unique event.