Most HDG stories aren't specific about the order in which they happened but there are general era's that they are set in! These are very general time periods based on narrative usage. Folks like writing about terrans meeting gay plampts (and falling in kinky love) and these era's center around that time period because of that.
Check out the Works page for the full list of canon works, spaning many of these eras!
Stuff happened, uh about 4 centuries of stuff since the present day, nothing is super concretely canon here. Some stuff that happened in this time includes: the discovery of exotic matters, terran jump drive got invented. Oh and Terra's biosphere collapsed, and global warming got really bad which accelerated the desire to be not on earth anymore. Eventually the Terran Accord formed an imperialist government that took over all the various nation states into one big capitalist empire.
As the setting is about kink with the affini, this isn't an era that has really been explored and is difficult to write about canonically (its vague on purpose!).
After the first signs of an xeno civilization (the Rinan Community), rumors sir for 3 years before confirmation that extraterrestrial life exists. Xenophobic paranoia is co-opted by the Accord's imperialist tendencies to pass the Terran Cosmic Navy Security Act, and the navy promptly commits an annexation and atrocities on the xeno civilization
There aren't really stories set during this time but many feature flash backs as this is the era during which most terran characters grew up!
The Affini Compact arrives at the edge of terran space, they become a rumor in the outer colonies, ONCI begins many secret weapons projects after confirming their existence. The Navy ramps up recruitment and production of ships in anticipation of a new xeno threat to conquer. Affini formally begin their Cotyledon program, with lost dying terrans they find trapped around the edge of terran space.
For the larger Accord, most citizens knew nothing of the clandestine operations taking place.
The three year war starting with the formal reveal and diplomatic request between the affini and the terrans. After both sides realized there was no peaceful resolution, the affini launched a full scale pacification program to save the terrans from their horrible living conditions(and also to domesticate some to keep as pets).
Due to the affini caputring planets along the way, some experianced the affini's societal overhaul and transition to a post-scarcity society earlier than others. Some post take over stories take place during this time.
The Accord formally surrenders to the affini with the signing of the Human Domestication Treaty and signal to all planets, stations, and navy ships that the war is over and the affini are in charge. The government is dissolved and replaced with the Terran Protectorate which has very limited legal capabilities, while the affini manage the more complex societal overhaul and transition to a post-scarcity society. During this time, many ship captains ignored the armistice and began a gruella war against the affini compact.
With about 99.999999% of all terrans having been brought under the fold of the Affini Compact, everything just sort of went well as the lasting generational traumas of capitalism and terran imperialism got fixed by post-scarcity communism under the vines of big kinky gay plants. Everything just sort of got chill and pleasant for uh approximately 331,896 years until the affini fixed reality itself with a universal ascension.