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The idea that the universe is expanding and that there is no center of the universe never made sense to me until a few years ago. I had naively thought that they meant that the boundaries of the universe are moving outwards so I couldn't figure out why there couldn't have been a center of it that still exists. But they mean that everything inside the universe (even the space itself) is expanding. They literally mean that the distance between things (everything) is getting larger. So the place where the big bang occurred is everywhere in the current universe. Think of the big bang filling the entire (but very tiny) universe when it occurred. Then it expands tremendously fast as it continues to do so now. The distances between everything in it continuously grows at about the speed of light and the space between things increases, too. Even the wavelength of the light from the big bang becomes longer because, heuristically, the distance between crests of those light waves increases tremendously. This last part was the hardest for me to grasp.
I can't help but think of John Neihardt's book Black Elk Speaks where the author relates Black Elk's vision which he had on Harney Peak (the center of the world). "'But anywhere is the center of the world', he added."
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