GRK: ἡμᾶς ἐν ἀρχῇ
KJV: …us at [the] beginning.
NO ARTICLE Philippians 4:15 (dative
GRK: ὅτι ἐν ἀρχῇ τοῦ εὐαγγελίου
KJV: in [the] beginning of the gospel,
Firstly, I do not have access to textual variations on article inclusion/exclusion for Daniel 9:21 in the LXX. Scribes definitely do play around with articles a little in subsequent centuries so it is a possibility that the articular version we read today was not originally articular.
Secondly, when you look up the Hebrew word used in Daniel here, בַּתְּחִלָּה֙ it is not the same word as used in the Hebrew, original, version of Genesis 1:1 בְּרֵאשִׁ֖ית, to which all scholars would agree there is at least some connection for John’s prologue writer. And yes, before you ask, the LXX also does indeed commence Genesis with the anarthrous “En arche” (no article). The Hebrew used for this idea is found in three other locations in the Old Testament, all of them in Jeremiah. However, only one of these, Jeremiah 26:1, is translated in the LXX as “En arche”. The other two Jeremiah references seem to show evidence of serious textual corruptions, I presume, into the Septuagint tradition because the book of Jeremiah seems to differ generally and significantly beyond this point between the Hebrew and its Greek translation. I should look into this more, but it is no longer of relevance to the current investigation.
But that should not satisfy, as we need to look at arche in its other forms and without the preposition “en”, which could affect how the need for the article applies is in Greek. However, we shall see that there too, a distinctive pattern will still emerge, albeit with a few more explainable exceptions.