Nobody can retain the material that way. Each thing you learn has to be attached to other concepts you already have, and your skills build on one another.
Nobody teaches Peano's axioms of arithmetic to kindergarteners; they're still learning how to identify shapes, to compare quantities. When they eventually learn even the simplest proofs, they'll build on the basis of careful attention to detail that they learned while mastering basic arithmetic.
Nobody teaches general relativity on the first day of college-level physics class. Students are still learning calculus at that point; even if they already had a calculus course, this is their first opportunity to apply it.
And nobody teaches the fundamental proofs of calculus on the first day of calculus class; you can use sloppy language like "infinitesimals" to establish a good intuition for how to use derivatives and integrals.
If you tried introducing this material from the bottom up, it wouldn't take. But if I'm wrong, sure, go try it and see how it works.