Your question is nonsensical. Poor BibChr — you're laboring under both a semantic and a temporal error!
1. Semantic: You are using “deity” as if it were an aspect of Jesus Christ, as if deity was a property possessed by or related to Christ. This is not only heretical (Nestorian), but semantically incorrect. “Deity” is not something that Jesus “has”; it is What He is. Deity = Jesus. The Man, Jesus, cannot be separated from the Second Person of the Trinity; He has no deity, he is Deity. To ask if Jesus' Deity existed before Mary is like asking if Jesus existed before Jesus — it makes no sense.
2. Temporal: Deity is God. As such, it is eternal — outside of time and space. To ask if Jesus' Deity existed “before” Mary or anything else makes no sense; something that is eternal exists identically at all times and in all places. Jesus Christ was, is, and forever shall be; he never began to exist, nor will He end. he simply is. The physical fact that something Eternal was born and has a mother is beyond human reason, which is why the Church has always referred to the Incarnation as a Mystery. We need not understand it; we need only accept it on faith.
Don't feel too badly about this. Confusion about the nature of Jesus Christ is only to be expected. As the Person at the intersection of the Eternal with our world of space and time, our Lord and His Nature are things we limited humans will never fathom completely. We must simply accept Jesus for Who He is: a Person, fully human, yet fully divine; Eternal God, born of a human mother, who is our Lady.