You can't really, by definition. By the same logic you should be able to store 1 cubic meter's worth of data storage cube into a 1 cubic micrometer of data storage cube, which in turn could be stored in a smaller cube ad infinitum.
Going by the same logic you could store all entropy of the universe in an infinitely small cube which is not possible unless the universe had zero entropy.
Sort of, according to the holographic principle. Since there is a limit on information density in space, you should be able to reduce a 3-dimentional volume to a 2-dimentional digital data structure. https://en.wikipedia.org/wiki/Holographic_principle
Tinsy nitpick. The universe technically didn't exist back then (at least not in the form of spacetime), I believe. Existence itself was confined to a singularity which then expanded with tar -xzf singularity.tar.gz
Going by the same logic you could store all entropy of the universe in an infinitely small cube which is not possible unless the universe had zero entropy.