Evolution explains design without a designer.
The objection, in full
Paley's watch was the strongest pre-Darwinian argument. Darwin disposed of it. Random mutation plus non-random selection produces the appearance of design from below. We don't need a designer for the eye, the hand, or the human.
Biology is the study of complicated things that give the appearance of having been designed for a purpose.
or, in plain terms —Evolution killed God.
Evolution explains the watch. It does not explain the watchmaker's tools.
Even granting the full Darwinian story for biological forms, you have not addressed: why the laws of physics permit chemistry, why the constants permit stable matter, why the universe began at all, why mathematics describes it, why minds exist that can do the science.
The teleological argument has long since moved upstream of biology. The question is not "who designed the eye" but "who set the stage on which design-by-selection can happen."
And the modern fine-tuning literature — Penrose, Rees, Carter — is not theological propaganda. It is mainstream cosmology asking the same question Aquinas asked, with bigger numbers.