The Twenty Second, Twenty Third And Twenty Fourth Centuries

"22nd C  The discovery of hyperdrive makes interstellar travel feasible early in the twenty-second century. The Breakup sends humans off to colonize the stars, often to preserve cultural identity or to try a social experiment. A loose government called the Solar Commonwealth is established.
"Hermes is colonized."
-Sandra Miesel, Chronology of Technic Civilization IN Poul Anderson, The Van Rijn Method, New York, 2009, p. 612.

Only one story, "Wings of Victory," about first contact with Ythri, is set in the twenty second century. Miesel's Chronology note for this story reads:

"The Grand Survey from Earth discovers alien races on Ythri, Merseia, and many other planets." (ibid.)

- and some of those other planets are named in "Wings of Victory."

Mirkheim informs us that the Breakup made the O'Neill colonies obsolete but that the colonies remained in their orbits and that the companion habitats called Hiawatha and Minnehaha still held working populations at the time of the Polesotechnic League Council of Hiawatha two centuries later.

Thus, Technic civilization begins in the twenty first century and the Solar Commonwealth in the twenty second. Several other major features of the later League period also begin in the twenty second century:

hyperdrive;
extrasolar colonies, including Hermes;
contact with Ythrians, Mersians and other races.

According to the Chronology, the League is founded as a space merchants' mutual protection society and the planets Aeneas and Altai are colonized in the twenty third century and the planet later called Avalon is explored in the twenty fourth century. No story is set in the twenty third century and only "The Problem of Pain," about the exploration of Gray/Avalon, is set in the twenty fourth century.

Thus, to summarize the History so far:

21st C "The Saturn Game"; Technic civilization.
22nd C "Wings of Victory"; Breakup; Commonwealth; Grand Survey.
23rd C  League.
24th C "The Problem of Pain"; Gray/Avalon.

Four centuries; three short stories; no story about the founding of the League.

The League must have been founded at some time but I am not sure how we know that this happened in the twenty third century? As far as I am aware, "The Problem of Pain" does not mention it.