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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

But assuming the universe has an entropy smaller than one, couldn't the data be compressed ?

I thought this is what black holes did.

Sounds like write-only media.

Hmm ... go back 13.5 billion years in time and that is exactly what was the universe back than.

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.

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