It happened over time.
1) The way the U.S. electoral system is structured, two parties is the “equilibrium point” (to use a flawed concept). Factions that in other countries, with other systems, would be in their own party end up as part of a big coalition party (not that I endorse a multiparty system; most of these are even worse, though for other reasons) because everything is set up around having a majority and winning the presidency: it’s a binary system so it produces a binary dynamic.
The most that can happen is what happened a couple times early on: the rise of a new party causes the collapse of one of the older ones (or, conversely, the collapse of one of the older ones opens up space for a new one to rise). Creating new parties is hard, and is made harder all the time (see below), so usually now people/groups who want a party simply take over one of the existing ones; this method first happened in 1896, with the takeover of the old Democratic Party by Bryanite radical populist-progressives, who shifted from the Republican Party (and, conversely, this takeover caused groups that were formerly Democrats to shift into the Republican party) (a switch described by Rothbard in one of these lectures here, though now I forget if it is most fully detailed in “The Decline of Laissez Faire” or “The Rise and Fall of Monopolies,” or “Tarrifs, Inflation, Anti-Trust” – all I do remember is that though “Pietism and the Power Brokers” is really good, as I remember, the 1896 party realignment is detailed most fully in one of the other lectures).
Anyhow, two-parties is basically the product of how the U.S. electoral system is set up, and it is possible to avoid that particular trap, but not without falling into another (such as establishing a system that is more conducive to multiparties, the product of which usually is endless coalitions, usually made up of the same parties that form a coalition, with small single-focus parties then demanding, as a price of their participation in the coalition, significant control over their pet issue, and the position they hold on that pet issue may be one where 80% of the rest of the electorate opposes them, but they get their way anyhow. Another usual dynamic of seriously multiparty systems is that because either the coalitions are eternally “stable,” you basically get the same policies no matter who you vote for OR they’re eternally “unstable” – that is, swings are so wild and coalitions so fragile that the “governments” (that is, the elective aspects of them) collapse frequently; in either case, bureaucracies end up having even more control – and I bet you didn’t think this was possible, but it is – over policy than under our system. Such multiparty states are controlled almost entirely by the Permanent Party of Government, despite any riotous political activity in the streets).