Alexander Hamilton, infamously, died of a gunshot wound in a duel with Aaron Burr, in the year 1804, at the age of 47 or 49 (records are unclear as to which year he was actually born). Hamilton was one of the younger Founding Fathers.
Andrew Jackson's Presidency ran from 1829 to 1839. Had Hamilton lived to see Jackson's presidency, he would have been in his mid-70s to early-80s. Although medicine was much less advanced and lifespans tended to be shorter than today, Thomas Jefferson lived to age 83. Benjamin Franklin lived to age 84. John Adams lived to age 90. Living to a similar age would have been quite plausible, particularly for someone with Hamilton's financial resources and personal energy.
So: a white-maned Hamilton delivering passionate speeches defending the Bank from Jackson's efforts to destroy it certainly could have happened.
Good job, Dall-E.