I would not agree with that because it's pantheism.
One meaning for His Face being everywhere is that everything is turned towards Him whether they know it or not, since He is the giver of being. It does not mean a literal encapsulation or identification of the Infinite with the finite.
Rather, closer to your sentiment from an Islamic theological perspective is to say that what we experience in the universe is an interplay of His attributes since He is the causer.
> Quran 2:115 states that wherever you turn, there is the Face of Allah.
So Allah is everything or at least he is IN everything. The universe is everything.
> the Quran states that He specifically created mankind to know Him.
Mankind experiences Allah, the universe.
Would you agree with this kind of mapping or am I making any unjustified leaps here?