You do realize that we have evidence of the Big-Bang right?
Anyways, on to my wall of text:
When all matter "dissolves" into radiation (yes, such a thing will happen eventually, that is a fact), that means everything moves at the speed of light because radiation is light. When everything moves at the speed of light there is no such thing as time because of general and special relativity (relativity has been proven!). And without time there's no such thing as distance, meaning that without distance everything is in one infinetly small place. It's not the same as a black hole besides perhaps the singularity, but we don't know much about the physics of black holes. Back to the point, When there's no such thing as distance, when everything is in the same infinetly small spot, that means that all energy, all matter in the universe is just there, that infinetly small spot is the "seed" of the big bang. The big bang it self then happens instantly and after forever (yes, both at the same time, because time doesn't exist before matter exists.). Understanding what actually triggers/triggered the Big Bang is really hard/impossible, but there are hundreds or thousands of physicists working on figuring that out.
Note that this is just one of multiple theories, but it's the one that I've personally found as the best on this matter. (I have no qualification to decide the "trueness" of theories though).
