One wonders here if the preposition on in “the people might look forward on the Son of God” might not be an error for “the people might look forward to the Son of God”, as in the clause later on in this verse: “that they might look forward to him”. The preposition to is what we expect here; elsewhere in the text there are seven other occurrences of “to look forward to X” (including the one later on in Alma 13:16), but there are no other instances of “to look forward on X”. There are, however, four occurrences of “to look forward unto X” and three of “to look forward for X”.
Interestingly, Literature Online has a few examples of the expression “to look forward on X”, including several clear examples from Aphra Behn, who wrote in the late 1600s (accidentals here regularized):
There is also an example written by the American poet William Cullen Bryant sometime between 1841 and 1844: “thou lookest forward on the coming days”. Thus there is evidence for “to look forward on X” in addition to the more common “to look forward to X”. Here in Alma 13:16, the critical text will maintain the preposition on in “the people might look forward on the Son of God”.
Summary: Maintain in Alma 13:16 the unexpected preposition on in “the people might look forward on the Son of God”; such usage can be found in Early Modern English as well as in 19th-century American English.