Here the 1830 typesetter added the relative pronoun that, probably accidentally. Elsewhere in the Book of Mormon text, when the time is followed by Jerusalem within a few words, that occurs 11 times but is omitted 6 times:
One of these examples involves manuscript variation:
Since either reading is possible for Jacob 1:1, there was no strong motivation for Oliver Cowdery to have emended the text here. Rather, the correction in Jacob 1:1 (with somewhat heavier ink) is probably the result of Oliver’s proofing of 𝓟 against 𝓞. For more discussion, see Jacob 1:1.
So there is nothing wrong with the earliest reading in 2 Nephi 1:24 (for which the relative pronoun that is lacking). This instance gives us a seventh example without the that.
Summary: Remove the intrusive relative pronoun that in 2 Nephi 1:24; in the Book of Mormon text, we have instances of sentences both with and without that after the prepositional phrases “from the time” and “to the time”; for this reason we follow the earliest textual sources in determining whether or not that occurs in this context.