This will not be constructive unless you stop using a rather pedestrian and ambiguous definition of "algorithm". I'm using it in a very strict sense. Let me say it again:
Everything that exists is algorithmic information. A rock, a tree, a cloud of hydrogen atoms floating in interstellar space, space itself. If algorithmic information implies "design", then your definition of "design" is meaningless since everything that exists in all possible spaces is "designed" by definition. We do not need a new word for "exists" in mathematics.
The more basic problem is that "design" is another one of those ambiguous and fuzzily defined "I know it when I see it" terms, like "alive". Until you come up with a strict and unamibiguous definition of "design", it cannot be used as a term in any kind of rigorous theoretical construct.
(The even uglier problem is that the pseudo-mathematical term "design" as it is being used her runs afoul of the Invariance Theorem, which makes it discardable ipso facto.)
Again, the assertion, tortoise: "Everything that exists is algorithmic information." It should be obvious to you that "everything that exists" is also something more than algorithmic information -- even given the case that your assertion is true. The reduction to algorithm in the sense you seem to indicate would drain all the life out of the world, leaving only a sterile machine in its wake. Life itself would become reduced to an abstraction.
I haven't given a definition of "design." But if I were to do so, it would not take the form: "everything that exists in all possible spaces is 'designed'... for that would not be a definition of design, rather it would be an (implicit) definition of "tautology." Any definition defines. The question is whether the definition is "any good" as a description of reality.
You do seem to give a definition, of Universe: the Universe is that which is specified by/reducible to an algorithm. And as for this result, it really doesn't seem to matter much in what "very strict sense" you are using the word "algorithm." Now it seems the Invariance Theorem applies to correlated movements of points in mathematical spaces; But life is more than movement in mathematical spaces, correlated or otherwise....
This -- life -- is the part you always seem to want to drop out of view. Notwithstanding, the fact that there is an invariant character to such correlated movements indicates a universal behavior; and if the behavior is universal, this suggests it cannot have arisen by accidental means.
Or so it seems to me, for whatever it's worth to you; and I suspect that approaches zero at the speed of light.