The term ‘God’ in itself is perfect, so the phrase ‘perfect or fully God’ is irrelevant. But Man is not perfect, for all men have sinned and have become imperfect. Jesus, when He was on earth, was perfect God and perfect man. The Bible says that ‘Jesus is the same yesterday, today and forever”. If Jesus was God yesterday, He is God today also and will be God forever. It is impossible for God, to not be God but it is not impossible for God to be a man.

However, Jesus, while He was God, lay aside all His powers, abilities and privileges as God, and came and lived on this earth with all the limitations and restriction of a man. The reason being that Jesus came to this earth to live a life as an example for all, and to die as the penalty for the sins of all mankind.

At the same time, Jesus is an Almighty God. The Word of God declares that Jesus has all the Characters which only God has (Omnipotent, Omniscient, and Eternal). Not only that, after His resurrection Jesus himself publicly proclaimed that He was God, thus proving that He was God himself.

So to answer how can Jesus be God and man at the same time?  It is not impossible for God to be a man while still being God, nor does the Bible say it is impossible.