The original manuscript is not extant here. While copying into the printer’s manuscript, Oliver Cowdery initially wrote “in the commencement of the reign of Zedekiah”, but then he corrected the manuscript by supralinearly inserting “first year of the”. There is no change in the level of ink flow, which implies that the correction was immediate and reflects the reading of the original manuscript rather than editing on the part of Oliver. There really would have been no motivation for the scribe to have added this particular information about the year unless these words were in 𝓞.
The shorter expression is found twice in 1 Nephi 5:12–13, both times as “from the beginning even down to the commencement of the reign of Zedekiah”. There is no need in this later passage to refer to “the first year” of his reign. Elsewhere, the text often refers to the commencement of a particular year in the reign of the judges, as in the following example:
Generally, I will comment in this volume on manuscript corrections that suggest either editing or scribal difficulties. Such difficulties often provide evidence for determining the original text for that passage and elsewhere. If a manuscript correction appears to be immediate and only the result of the scribe’s desire to copy his text correctly, that correction will probably be silently passed over.
Summary: Accept the supralinear insertion “first year of the” in the printer’s manuscript for 1 Nephi 1:4 since apparently the scribe’s only motivation here was to accurately copy the text from 𝓞 into 𝓟.