By randomness, do you refer to an explanation of biological evolution, or of the universe's origin?

If you refer to evolution, then you're mistaken . . . no serious biologist thinks that adaptive evolution is driven by random processes. The generation of variation (by mutation) is effectively random - by which I mean that mutations occur at random with respect to their effect upon organisms (we've had this precise discussion before). Non-random processes, on the other hand, 'select' variants which happen to be better at making copies of themselves, and thereby govern adaptive evolution.

If you refer to the creation of the universe, then I'm not really equipped to enter the discussion, as I'm no expert on astro-physics . . . it's hard to believe that anything with inherent order is created totally randomly, but, on the hand, a non-random process doesn't by any means imply the existence of divinity. In other words, "non-random" is not synonymous with "Creator", as you seem to imply.