You don't. The DS is pretty unique for a cartridge based system in using a file system (the GBA before it did not, at least outside of homebrew). Older systems will tend to bundle the files/sections together.
There are various tricks you can do to find things on various non filesystem based systems; things like the GBA binary finding technique, fingerprinting (again on the GBA there is the sappy sound format that can be detected and some of the really advanced game specific stuff will go a step further still for all sorts of formats) and right through to tracing, backwards searching (take the palette from memory and search the ROM for it), not to mention good old relative search and just pressing page down a lot in a tile editor. At no point though will you be able to explode it into various files and put it back together later.
Theoretically one of the older systems could have had a file system made for a game, it would not really pose much in the way of a technical challenge, but I am struggling to think of a single non homebrew example for any system that did not have one by default.