The first side scrolling game was released on the Famicom after two years or am I wrong?
Let me clarify the role of the memory mapper and how scrolling on the NES works. Perhaps saying the NES wasn't built for scrolling or single screen games is going a bit too far. The NES was still designed mainly to accommodate single screen games like Mario Bros or Donkey Kong, but it had some unique quirks at the time that enabled games like Super Mario Bros to scroll
The NES can set up pages of screen resolution into various configurations using mirroring modes. You can think of the screen real estate on the NES as being two screens big, either arranged in a horizontal arrangement or a vertical arrangement. The reason Nintendo did this was to allow for scrolling high score tables or screens that "moved" onto each other, like Zelda or the title screen for bubble bobble.
Conventional computers at the time allowed only for full width character scrolling, but the NES PPU had an offset for pixel scrolling of individual characters. This was meant to let one page transition to the other, again, like how Zelda's screen transitions work.
Games like Super Mario Bros would use memory mappers to move a seam of 8x8 character blocks off screen over once they reached the edge of the screen. The idea was to scroll by pixel the two screens until you reached the edge of the right most screen, at which point the entire scroll would reset to 0, and the position of the "seam" would shift so that you never noticed. Early mappers, like in Super Mario Bros 1, only allowed this seam to move in 1 direction. Eventually, more advanced mappers allowed the seam to move in multiple directions.
Multidirection scrolling on the NES was essentially impossible. The way games like Mario 3 got away with it was by defining the mirroring mode in vertical space such that every screen was 2 screens tall. Then, expecting overscan to hide the effect, the right-most column of the screen was devoted to the "seam." The game would offset the horizontal pixel arrangement of the screen up to 1 column of tiles until it'd snap back to place. This is why, when played on an emulator, you see artifacts on the right side of the screen in Mario 3. This is also why, excusing the vertical scrolling levels in World 7, all levels in Mario 3 are 2 screens tall and no taller.
Mario 2 got around this by switching mirroring modes at points. The levels would be arranged horizontally until you reached a point where it'd need to scroll vertically, at which point it'd become a vertical orientation. Mario 2 never scrolled in 2 directions at once.
Contrast this to systems built for multi-directional scrolling, like the Sega Genesis, which has hardware registered to scroll in both directions. Scrolling on the NES is rather one large trick.