The question here is whether the original manuscript had that after “it came to pass”. The printer’s manuscript has the that while the 1830 edition lacks it. The same variant is found later in this part of the text where both 𝓟 and the 1830 edition are firsthand copies of 𝓞:
In that instance, the scribe in 𝓟 was the unknown scribe 2, while here in 3 Nephi 8:5 the scribe was Oliver Cowdery.
For the phrase “come to pass”, we have the following cases in the history of the text where a that has been added by the scribe for 𝓟; there are four clear cases, and in each one the addition was momentary:
In the second of these cases, scribe 2 of 𝓟 initially wrote the correct when, but then he wrote inline that when. Here he seems to have become distracted in his copywork, and he ended up repeating the subordinate conjunction when and also adding a that (virtually immediately scribe 2 crossed out the extra that when). In the third case, Oliver Cowdery added the that apparently in anticipation of the that which originally followed the subordinate conjunction after (Oliver initially omitted this particular that in 𝓟). The first and fourth cases appear to be straightforward instances of momentary insertion of the that by Oliver. Ultimately, the evidence for the scribes adding the that is rather meager, especially since all four of these cases were corrected in the manuscript. On the other hand, there are nine clear cases where Oliver Cowdery accidentally omitted the that after the phrase “come to pass”, of which one was permanent (see the list under 3 Nephi 1:22).
Turning to the 1830 typesetter’s practice, we find that there are two cases where he omitted the that after the phrase “come to pass”; in both cases, the text involves an Isaiah quotation:
In the second case, John Gilbert consciously removed the that (he marked its deletion in 𝓟). In both of these cases, the corresponding Isaiah passage in the King James Bible lacks the that immediately after “come to pass”:
The evidence suggests that Gilbert consulted his Bible when he decided to omit the that in these two cases (see the discussion under 2 Nephi 17:21 and 2 Nephi 24:3–4). Yet otherwise, the 1830 typesetter never deleted a that after the phrase “come to pass” (see under Alma 58:14 for one case where he added the that). Thus one can argue that here in 3 Nephi 8:5 and in Mormon 1:8 Gilbert was not responsible for the textual variation. Instead, it is more likely that Oliver Cowdery accidentally added the that in 3 Nephi 8:5 and scribe 2 of 𝓟 accidentally added it in Mormon 1:8. Note, by the way, that one could argue that the extra occurences of that in 2 Nephi 17:21 and 2 Nephi 24:3 could be transmission errors on the part of Oliver, either in 𝓞 or 𝓟, thus supporting the hypothesis that Oliver added the that here in 3 Nephi 8:5. But internal evidence elsewhere in the text actually supports the extra use of the that in those two Isaiah quotes, as discussed under those passages.
Elsewhere in the textual history, we can find specific evidence for either adding or deleting the that between “come to pass” and a following prepositional phrase headed by in. We have, for instance, two cases where Oliver Cowdery initially omitted the that in 𝓟:
There are also a number of cases of either adding or deleting the that in printed editions after the first one (most of these appear to be accidental):
There is some internal support for the shorter reading in 3 Nephi 8:5. Note that here we have an extended prepositional phrase headed by in that specifies the year, month, and day of an event. Elsewhere in the text, when we get such a detailed specification with references to these three time elements, we never get the that between “come to pass” and the following complex reference to time:
There is also one example involving month and year: “and now it came to pass in the second month of this year there was brought unto us many provisions” (Alma 56:27). This systematicity argues that in 3 Nephi 8:5 the original text did not have the that after “it came to pass” and that Oliver Cowdery added the that when he copied from 𝓞 into 𝓟; thus the original text probably read as follows:
See under Mormon 1:8 for further discussion regarding the lack of that after the phrase “come to pass”.
This decision in favor of the shorter reading for 3 Nephi 8:5 and Mormon 1:8 (that is, without the that) agrees with the statistical preference for the shorter reading elsewhere in the text. Excluding these two cases, we find that in the earliest text, given the phrase “come to pass” and a following prepositional phrase headed by in, there are 38 cases with an intervening that and 63 cases without it. More specifically, if the prepositional phrase headed by in is followed by an existential there-clause, we get 11 instances with that and 21 without (once more we exclude these two cases from 3 Nephi 8:5 and Mormon 1:8 in the count). In theory, of course, either reading, with or without the that, is possible here in 3 Nephi 8:5 and in Mormon 1:8. But the occasional tendency of Oliver Cowdery and scribe 2 of 𝓟 to accidentally add the that immediately after the phrase “come to pass” supports the decision here to reject the that in these two passages.
Summary: Accept the current reading in 3 Nephi 8:5 without the subordinate conjunction that after “it came to pass”; there is some evidence from transmission errors by Oliver Cowdery that he could have accidentally added the that here when he copied from 𝓞 into 𝓟; usage elsewhere in the text supports the lack of that when a following adverbial phrase provides a complex reference to the time of the event.