In both the Genesis "beginning" and John's "beginning" start out the same way. The definite article has been supplied. The actual Greek is "en arech--that is, "in beginning."
The "Word of God" thus was there before the creation of the space-mass-time universe, so that John's "beginning" even antecedes the Genesis "beginning," extending without an initial beginning into eternity past, before even time was created. Note also John 17:24, where Jesus, in His humanity acknowledged that He was with the Father, and loved by the Father, "before the foundation of the world."
John 1:2, with God. The "Word of God" (i.e., Jesus Christ) was God, yet also "with God." Thus God is both personal and plural (in a uni-plural) sense only in terms of the doctrine of the Trinity).
John 1:3 made by Him. This is an emphatic statement declaring that Jesus Christ, BEFORE His incarnation, had made everything in the universe. He is the God of Genesis 11:1, the God of all creation. Furthermore, note that "all things were made." They are not now being made, as the concept of evolution requires.
This is all backed up by Colossians 1:16; Hebrews 1:2-3; Hebrews 1:10 and other verses dealing with creation like Revelation 3:14.
So, both verses, Genesis 1:1 and John 1:1 start out the same way. Yet the main thought in Genesis 1:1 is on WHAT HAPPEND "in the beginning," and in John 1:1 the emphasis is on WHO WAS THERE in the beginning. AS a side note, and strictly speaking the Godhead was involved because all of God/Deity is mentioned at Genesis 1:1. But specifically speaking, we are introduced to the person of the Holy Spirit at Genesis 1:2. (Most of this information came from the "Institue Of Creation Research.)