Most of the time, an image that size is a banner or poster, and it's typically a vector image, done in Illustrator or Inkscape. I've only designed one poster-sized map, and it was done in Illustrator.
You don't necessarily need 300 dpi in a print that size. Consider the estimated viewing distance when setting up your document. If the map isn't intended to be viewed at arm's distance or less, then you can reduce the resolution accordingly.
By the way, 48" square is huge. You may want to give yourself a reality check by actually laying that out and seeing if you need it to be that big. My poster print was, I think, 36" x 24", and that was about the right size for a good poster map. It could be unrolled on the table without going off the edges or hung on the wall and viewed from several feet away fairly easily. And since it was intended to be viewed from a fair distance, I exported it at, I think, 200 dpi, making the rasterized file 7200 x 4800, which most reasonably modern computers can handle.