The original manuscript has the noun phrase a retreat rather than the infinitival to retreat (the reading of the printer’s manuscript as well as all the printed editions). Of course, either reading is theoretically possible.
Elsewhere in the text, there are three examples of “begin to retreat” but none of “begin a retreat”:
The noun retreat also occurs elsewhere in the text (seven times), but there are no other instances with the verb begin. The vast majority of cases of the verb begin are complemented by infinitive clauses, but there are a handful of cases where begin is complemented by a noun phrase:
The last two are highly significant here since march and retreat are semantically similar. In fact, “he began a retreat” in Alma 52:23 is indirectly supported by the nearby “Moroni … had began his march” (in Alma 52:15).
Oliver Cowdery probably copied “he began a retreat” as “he began to retreat” because of the much higher frequency in the text of “to begin to do something” than “to begin something”. On the other hand, there is little evidence that the reading in 𝓞, “he began a retreat”, could be a mistake for “he began to retreat”. There are no instances in the history of the text where to has been replaced by a. Clearly, “he began a retreat” is the unexpected reading, so it is not surprising that Oliver accidentally changed the a to to when he copied the text. Thus the critical text will accept the reading of 𝓞, “he began a retreat”.
We should also note that the use of the noun retreat in Alma 52:23 (“he began a retreat”) implies a controlled retreat on the part of Teancum’s army. A similar example of a controlled retreat is found in Alma 58:18 (as implied by the verb cause): “I caused that my men—those which were with me—should retreat into the wilderness”. The secondary reading in Alma 52:23 (“he began to retreat”) obscures this sense of a controlled retreat.
Summary: Restore in Alma 52:23 the reading in 𝓞, “he began a retreat”; the secondary reading in 𝓟, “he began to retreat”, is due to the much greater frequency in the text of “to begin to do something”, but this secondary reading loses the sense of a controlled retreat.