Toddlers are new little people with very little experience of life. They simply don't see a mess with the same critical eyes we do. But they do quite naturally try to imitate everything they see. Including attitudes. You won't be able to "make" a child this young do the work herself without starting a lifetime of struggle over who's in control, and loads of resentment on both sides of the struggle.
But she will eagerly imitate anything she sees you doing. If you initiate cleanup in a happy spirit, she'll participate in the same happy spirit. Attitude is everything (and not only for children, but for grownups, too.) So model happy cleanup procedures. I still do this with my 4yo grandboy, and we make cleanup fun for us both. He's just now getting to where he will clean up a mess when asked, and he still seems (often) to enjoy the process. Hooray!
Yup, you're crazy busy and have other tasks to attend to. You'll still be shooting yourself in the foot to make this a major issue now. You might try loosening your idea of what an organized home needs to look like for a few years.