BusyBeaver(6) Is Quite Large

If you treat the observable universe as a closed system, you could try to apply the Bekenstein bound using - R ≈ 46.5 billion light-years (radius of the observable universe) - E ≈ total mass-energy content of the observable universe

The mass-energy includes ordinary matter, dark matter, and dark energy. Current estimates suggest the observable universe contains roughly 10^53 kg of mass-energy equivalent.

Plugging these into S ≤ 2πER/ℏc gives someting on the order of 10^120 bits of maximum information content.

S ≤ 2πER/ℏc

S ≤ (2 × 3.141593 × 3.036e+71 × 4.399e+26)/(1.055e-34 × 299792458)

S ≤ 2.654135e+124

S ≤ 10^120

So, no.