the federalists basically became the National Republicans, then the Whigs, then most northern whigs became republicans, everyone in the south became a democrat
then between 1896 and 1980 the democrats and the republicans basically swapped political positions, with the democrats becoming more liberal and the centre-left party and vice versa
for the first party system to be preserved, maybe just have Jefferson elected in 1796, without the disaster of the John Adams presidency, the federalists might have had a chance, once the Virginia dynasty of presidents (Jefferson, Madison, Monroe) had all served