For those who do not believe that the Universe was a product of intelligent design, what qualities of the Universe would you expect to be different if it was intelligently-designed? What would have to be different about the Universe so that intelligent design would be considered the most likely explanation for these qualities? Take note that I am not talking about absolute proof, just whatever evidence would be sufficiently strong to lend weight to intelligent design.
I think this is a very pertinent question and one of the reasons I don't accept intelligent design as a reasonable conclusion. Simply put: I don't think there is an answer. The Universe could exist in
any form and it wouldn't exclude or preclude the possibility of design in general. If a God exists, in any form, there's no way to categorically demonstrate that said God didn't "design" the Universe in whatever form it is, or isn't in some way behind the natural processes that we observe are responsible for the Universe. Heck, "God's method" could in fact
be natural processes, so the difference may indeed be non-existent. The assertion of design is an un-falsifiable proposition, at least if we assume a very broad and general definition of a designer.
However, there is a difference between "design" as a general assertion about the origin of the Universe and far more specific accounts of
creation itself. It's one thing to say "The Universe is designed", and quite another to assert "The Universe was designed in such a way as it was formed in six 24-hour periods, with all currently known lifeforms existent, via supernatural means". The first claim doesn't present a testable hypothesis, but the latter presents a series of claims that we can indeed test, so whether or not we should expect to see signs of design in the Universe entirely depends on what specific interpretation or method of design you are asserting.
For example, if you believe in a design process that specifically resulted in all species of animals appearing simultaneously, we would expect to see a fossil record in which all animals appear within a similar time-frame in the geological strata without any prior transitional forms or any indication of previous life. If you believe the Universe was designed in a very small time period and is no older than a few thousand years, we would expect to see facts that refute the geological and archaeological evidence of the earth's age, and that overturns our understanding of big bang cosmology. Please note that neither of these claims indicate anything about "design" in general, only
specific claims about exactly HOW the Universe was designed. Unearthing a fossil record that completely refutes the notion that all life appeared simultaneously as-is, doesn't rule out the
possibility of a design process which didn't require all life being created simultaneously. Demonstrating that the Universe is far older than a few thousand years doesn't rule out the
possibility of a design process which spanned over a far greater period of time.
In conclusion, the question of what we should expect to see in a "designed" versus a "non-designed" Universe is only a question that can be suitably answered by providing more specific, testable predictions within a framework of design, and as such is not a question that can be accurately answer by those opposed to the proposition of design in general, but is a question that has to be addressed by those advocating for a specific design framework.