Some years ago, a person with whom I was conversing tried to argue that ARXH in John 1:1a is timeless and dimensionless because the word is anarthrous there. Here is my reply to that claim:
What grammatical evidence do we have that ARXH when employed anarthrously, has a special or unique lexical content? I don't know how you feel about the issue of Johannine authorship, but I personally believe that the apostle John wrote both the Gospels and the three Epistles. If this is so, the opening verses of the first Epistle shed illumination on the Prologue of Jn 1.
EN ARXHi HN hO LOGOS KAI hO LOGOS HN PROS TON QEON KAI QEOS HN hO LOGOS (Jn 1:1).
hO HN AP' ARXHS hO AKHKOAMEN hO hEWRAKAMEN TOIS OFQALMOIS hHMWN hO EQEASAMEQA KAI hAI XEIRES hHMWN EYHLAFHSAN PERI TOU LOGOU THS ZWHS (1 Jn 1:1).
Please notice that ARXHS in the first Epistle is also anarthrous. Yet there is no indication that the writer is employing ARXHS in a timeless--from a human viewpoint--sense. He goes to great lengths to locate the ARXHS within history (within time). "From the beginning," the disciples "heard" "saw" "looked upon" and "handled" TOU LOGOU THS ZWHS. There is no indication of a dimensionless ARXH in the Johannine Epistle. This seems significant in view of the fact that ARXH here [Jn 1:1a] is also anarthrous. Of course, my argument relies heavily on a literary nexus between the Johannine Gospel and Epistles. But even if different writers composed these Scriptural works, 1 John 1:1 still serves as an example of an anarthrous ARXH that is manifestly historical.
The same can also be said of Jn 1:1:
"ARXH, HS, ARXOMAI: a point in time at the beginning of a duration--'beginning, to begin.' ARXH: EN ARXHi HN hO LOGOS 'in the beginning was the Word' or 'before the world was created, the Word (already) existed' or 'at a time in the past when there was nothing . . .' Jn 1:1" (Louw-Nida 67.65).