Yes, but you need to correctly identify the random piece in order to discuss whether there are alternatives to its randomness other than intelligence. If the random piece is genetic mutation within the given biosphere, then yes, if you hypothesize that randomness is an inadequate explanation for the results, then intelligence is not the only direction one need look toward. Two directions you can look toward are external sources of biotic information (e.g., panspermia) or external forces of influence (e.g., morphic fields). Neither of those are inherently intelligent design as they're formulated, although one might hypothesize a source of intelligence to account for them (just as one might hypothesize a source of intelligence to account for natural selection alone).
You are layering unproven hypothesis atop unproven hypothesis, but that's nonetheless the answer to your question. If randomness is inadequate, intelligence is not the only potential resolution.
There's yet another solution off the top of my head: the perception of randomness is an illusion; the universe is deterministic. That doesn't require intelligent cause either.
Were the universe to be deterministic and not of an intelligent design, then one must posit the universe itself as some prior, highly organized entity that spawns highly organized subsystems. That would beg the question, too, of the first organized universe, or the organizing principle that underlies it.
PS. The so-called "cosmic ancestry" hypothesis is a subset of this formulation.
And, as an idle aside, although in a much less methodical way than I intend to do so in our framework debate, I've here demonstrated the error that Alamo-Girl was expounding earlier: That any proposed solution to any given objection to the modern synthesis theory of genetic evolution is "intelligent design"...
Oh, and once again, that error is the fallacy of the excluded middle.
This has experimental consequences. So far, all the experimental evidence comes down on the side of randomess.
From a previously posted example: in a bunch of radioactive atoms, some decay, some sit around. The half-life for decay can be measured as can the probability of any given atom decaying in given time interval. In both theory and practice, it cannot be determined which atom will decay next nor when a given atom will decay. Were such a determination possible, one could separate the "hot" from the "cold" atoms and label each atom by it's scheduled decay time. Labelled atoms obey Maxwell-Boltzmann statistics whereas unlabelled one obey either Fermi-Dirac or Bose-Einstein statistic. Experimentally only the FD or BE have been observed.