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

Yes, and along the road we have accumulated some entropy.

Anyhow, that was a rather crappy answer, the "How much entropy does the "data about a volume in space" have?" answer basically captures it.