The normal style of the original text is to follow subordinate conjunctions (like because) with that. For instance, elsewhere in 1 Nephi we have these examples from the original text:
Such style is characteristic of the King James Bible:
In his editing for the 1837 edition, Joseph Smith generally deleted this archaic use of that after because, although a few examples are still in the current text, such as 2 Nephi 2:26: “and because that they are redeemed from the fall they have become free forever”. In the example from 1 Nephi 1:14, Oliver Cowdery had become so familiar with the expression that he started to write because that as he copied the text here from 𝓞 to 𝓟. This example also shows that the use of the that after because was variable in the original text, so in each case we follow the earliest textual sources in order to determine the original reading. For a complete discussion of both the edited and unedited examples, as well as ones without the that, see subordinate conjunctions in volume 3.
Summary: Follow the earliest textual sources in determining whether subordinate conjunctions like because should be followed by the archaic use of that.