The first 100 years after the collapse is a mess when it comes to dating events. We know a lot of things happened during this time however the exact dates with the exception of a few places are fuzzy at best. However what we do know for certain is that from the year 1AC to the year 5AC the collapse that happened in year 0 was technically still under way as during these years many of the old world governments were still around however they were on their last legs.
These nations were the United States, Russia, Japan, Ireland, Poland, Israel, Ethiopia and Afghanistan. However with the exception of Ethiopia and Israel, the rest will not be able to recover.
Though some historians argued that the US managed to sustain itself through the New Confederate States of America, however due to them not going through the same societal upheaval the rest of the world was forced to go through, they eventually collapsed in the 2nd century AC.
Some early nations of note to rise during this time would be New England, the Confederation of the Great Lakes (which was a large alliance of cities and counties that banded together against larger groups for mutual protection), Londinium, Sicily, Tunis, New Moskovy, the Kingdom of Brandenburg, the Warsaw State, the Han Clique, Kyoto, and the Bay ascendancy.
These powers would fight for survival against their neighbors until they were either destroyed or they evolved into something greater. In the late 1st century AC Great figures would arise around the world and begin the restoration of complex civilization. Wars would once again be fought with muskets and borders would eventually solidify.