Oliver Cowdery initially wrote the singular thousand; then later (probably when he proofed 𝓟 against 𝓞) he inserted a plural s at the end of thousand (the correction is with heavier ink flow). It is very probable that the original manuscript read thousands since we know Oliver frequently added and deleted final s ’s in his copy work (see, for instance, the discussion regarding borders and shore under 1 Nephi 2:5).
Elsewhere in the original text, the partially singular many thousand occurs only when it is immediately followed by a noun phrase:
None of these cases are followed by an of-initial prepositional phrase. On the other hand, instances of the fully plural many thousands preceding a noun phrase always have the preposition of:
These complementary patterns suggest that “many thousands of the Lamanites” is the correct reading for the Words of Mormon 1:14. If many thousand were correct, the connecting of the would have been omitted (giving “many thousand Lamanites”). Or perhaps a noun like men could have originally occurred between “many thousand” and “of the Lamanites”, although the phrase “men of the Lamanites” is rare and occurs only in Alma 62:15: “a large body of men of the Lamanites”.
Summary: Retain “many thousands of the Lamanites” in the Words of Mormon 1:14, which is Oliver Cowdery’s corrected reading in the printer’s manuscript and the probable reading of the original manuscript (no longer extant here).