What "beginning" did John intend us to understand?
The NEW Beginning, the beginning of the Gospel of Jesus Christ. Jesus is the author of our faith, that is, the author of the way of Christianity. He is the beginning because his ministry was that beginning. And this is the beginning John has in mind.

See The Trinity Delusion website:
http://www.angelfire.com/space/thegospeltruth/trinity.html

John 1:1
http://www.angelfire.com/space/thegospeltruth/TTD/verses/john1_1.html