The answer is an unequivocal no.
Because space and time are two abstract concepts that resolve to nothing in reality. Space and time have no boundaries for God, you or me to transcend! Space and time are not a house that you can transcend by walking out the front door and circling in the yard. There is NO front door to the universe. Or back door. Only objects have boundaries, and only can the internal structures of objects recede bounds. Those who irrationally assume that space is an object with a bound receding at C will have to explain that which space is receding into. Is space receding into the space of another universe? What is outside of space? More space?
Space lacks Form. Space has no dimensions since it is not an object of existence with shape and internal structure. Space refers to nothing. Space is a concept referring to the static distance between two or more objects of existence. The distance between two nouns of reality is also called spatial separation. Adam and his children came along and conceptualized space by associating objects via their brains. Unfortunately some have converted space into a noun of reality with a form and so now we have to deal with the patients of the insane asylum raving that the universe's bound is expanding at an ever increasing rate of acceleration into nothing! Hmm. How does God continue to move beyond space when it is expanding so quickly?
Theologians would do well to resolve the ontology of the referents 'space' and 'time' prior to making the strange claim that God transcends space and time. Then after their resolution they must define space and time. Then they should EXPLAIN just how God transcends space and time.
Time is the brain associating a succession of locations which an object or objects assume (motion). This is accomplished via the activity of the atoms or neurons responsible for memory. Location is the set of static distances from one object to all other objects. Like space, time has no bounds since it has no form. Time is all in your head. Time is a verb not a noun of reality. Humans get together and agree upon a scalar quantity to reference the motion of objects e.g. the day and then they arbitrarily divide this quantity into smaller quantities (hours, minutes, seconds, etc.). Time is a metric of motion or simply memory and motion. And it is good to note that children of Adam and Eve have no memory of all the locations of all atoms of the universe. The scientists are quite frankly insane when they presume to use a tautologous system to 'predict' the time of the network of atoms.
It is impossible for God to transcend space and time since time and space have no Form. This statement is at best poetic, and at worst irrational. A better statement would be to say that God defies our rational and well-defined notions of space and time. With God miracles are possible. For example God is an Object who is located at two or more locations in a single still imagined frame of the Universal Movie. God can be in multiple locations at will. And of course God is always in the Heaven, a system of objects that must necessarily be present in relation to all the astronomical objects of the our universe (otherwise Heaven could not be said to exist).
And yet the Heaven of God, or (IMHO) the parallel universe which God built up around Himself is not woven into our network of matter. But still the objects of the heavenly system must necessarily have distances in relation to all the astronomical objects of our universe. Like I said in a previous post . . . I would not be surprised the least if Heaven was right up beyond Earth. We would never see it since the atoms of our universe are not connected by the invisible mediator of light and gravity to whatever atoms may be present in the Kingdom of Heaven.
God is a singular type of Object that does not rely on space for His Form. It seems to me that God binds God from His immediate surrounding. This is in accord with reason impossible yet in a faith-filled conception it seems possible since God is One yet Three. The Three Personal Identities bind each other from their immediate surrounding in a singular eternal phenomenon that defies rationale. So when the Spirit is sent to the Earth . . . the Spirit is still bound from His immediate surrounding by the Father and the Son.
Before a theologian goes on to say: God transcends space and time I suggest he resolve whether or not space and time have Form or lack Form. Resolve the ontology of the referents, and THEN define the key terms space and time and THEN explain just how God transcends these ideas. Simply stating that God is Eternity is not good enough. Using the rationale: God is Eternity thus God transcends space and time is a meaningless statement. It is patently circular. What have we learned???
And by the way God did not create space and time.