To which beginning is the word ‘beginning’ (arche) referring in the Gospel of John, outside of the prologue?

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The standard reading of John 1:1

"In the beginning was the Word, and the Word was with God, and the
Word was God."

is that the beginning – ἀρχῇ (archē) – refers to the old beginning, i.e., the beginning described in Genesis 1. The word is repeated at 1:2.

However, John’s prologue is condensed and poetic language. This motivates an inquiry into how John uses key words, such as ‘beginning’, in the rest of his Gospel outside of the prologue, to better inform our reading of the prologue itself.

How is ‘beginning’ (archē) used throughout the Gospel of John, not only the prologue? Beginning as in ‘arche’ only occurs 6 times outside of Chapter 1. Does it usually refer to the Genesis beginning? Does it usually refer to a beginning (or beginnings) associated with the life and ministry of Jesus?