According to the "Chronicles of the Five Companions" volume 1 the Soulburst happened in late 2e578.
in "Season of the Dragon" and "Dark Heart of Skyrim" we meet some of the Companions freely moving around Tamriel. Could these storylines happened before the Soulburst ? Let's say 2e575 ? The same could be said for all the other DLCs and Chapters as we do not see Dolmens (Abyssal Geysers don't count).
The infamous arcane explosion in the Imperial City that happened in the Spring of 2e579 — a night of storms, and trembling terrain — as related by the Chorrol Crier, mentioned by Chancellor Abnur Tharn in his "Eulogy for Emperor Varen" and explained by Lyris of Skyrim in the first volume of her "Chronicles of the Five Companions", and others, I am sure. The “Soulburst” happened at the same time as a big piece of Aetherius fell to Nirn. Coincidence? It was the first major piece of Aetherius to fall in five hundred years. My name is Elsyna Seedgrass — I was born on 12 Evening Star 2e563 at the Redfur Trading Post in Grahtwood. When I was 3 years old my father brought home a senche-tiger cub. He is night-black with burning paws and most of my friends are afraid of him. We rapidly became friends, and I named him "Flame Leaper". His life span is about 20 years. I was orphaned a few months later and Valirr, the Khajiiti leader of the Hollow Moon Organization, took care of me. By my fifteenth nameday I had located all 10 wayshrines in Grahtwood, then I went my own way and moved to Auridon.Then I met the Prophet on 4 Rain's Hand 2e582.