The first new aristocracy would probably be House Small since they set themselves up as a ruler of Small World near the dawn of interstellar colonization.
Picking another example:
Per the House Davion Sourcebook, neo-feudalism was developing on New Avalon in the 2240s among its "first families." Around 2255, New Avalon's Second Covenant changed the role of prime minister from a 1-year term to a lifetime role. In the 2330s, New Avalonians were getting concerned that the Davion family was starting to act like a dynasty as one after another was elected to important positions like Prime Minister of New Avalon and President of the Federated Suns (and combined the separate roles of PM and President). In the early 2400s, Edmund Davion eliminated a lot of First Family and High Council power that culminated in near-absolute rule in c2415.
Simon Davion, who allegedly freed the Suns from the tyranny of Edward Davion, reformed the Suns into a non-hereditary aristocracy in 2417, the principality system. So that's the Suns announcement of a monarchy.
The other Houses were evolving aristocracies at that time, too.