Until human beings innovated methods of traveling long distances, they never even had the basic knowledge to think of outer continents ever existing.
That being said, it was not too long ago in our history that people believed that there was no outer planets, and that we were at the center of the universe.
Our understanding of space today is far different from what our ancestors taught thanks to technological advancement and research on space.
So to answer your question, which will be a simple and rather mundane reiteration of what the others have stated before me, we know not of whether they exist or not, much like extraterrestrial lives and Nessie. Quite obviously, this is mainly due to us lacking the technology or means of actually reaching or let alone observing the other dimensions. That being said, it does not necessarily deny the existence of alternate dimensions, just as much as we cannot deny the existence of fish in the ocean through scooping a cup of seawater and finding none inside it.
I personally wish, and I guess I do believe that there are alternate dimensions. :notzd: I have heard rumours of people and things disappearing all of a sudden, and they might have been sucked into a portal which leads to worlds different from ours.