There was no "conservatism" in the early United States. What there was was Toryism, which was associated with having opposed the Revolution and which, while clearly on the right, cut across groups that would today be viewed as all over the place on the scale of socioeconomic advantage. Inasmuch as seeking to conserve political and economic forms inherited from Britain (or replicate forms present in Britain) could be seen as "conservative", Hamilton was obviously more conservative than noted Reign of Terror apologist Jefferson, and he was indisputably reactionary and elitist regardless.
In Jefferson's America, an ideology based on urbanism, government bureaucracy, and the working class would be unfathomable; in Hamilton's America, it would be the natural left pole of national policy. And, indeed, it is.
In Hamilton's America the working class would never have gained the right to vote, and so such ideology would never stand an even remote chance.
They wouldn't have if Jefferson got his way either, so