In reading and re-reading a bunch of ID publications recently, this is something where ID is frustratingly vague.
There are a lot of ID arguments that center on basic biological machinery in the cell including the very formation of DNA. This makes ID sounds like an origin-of-life argument. And life began on Earth over 4 billion years ago.
But some of their other arguments around higher order organisms calls into question when and where the 'designer' was doing its designing.
For example
in this paper, Meyer argues that Cambrian-era life has hallmarks of design. That was over 500 million years ago or about 3.5 billion years after the origin of life on Earth.
In another paper, A.C. McIntosh tries to argue (poorly) that feathers and avian respiration are evidence of design. Based on fossil evidence, feathers have been around since at least 160 million years ago.
In yet a third paper, author Joseph Kuhn specifically references various systems in the human body that they describe as "infinitely complex" (as an aside, what the heck is "infinite complexity" supposed to even mean?); although many of these systems are also found in other animals.
All of this begs the question of what the designer actually did. Did they start life 4 billion years ago, sit around for 3.5 billion years twiddling their thumbs before deciding to zap in a bunch of new life? Did they decide to engineer feathered dinosaurs 160 million years ago? And then over a hundred million years later start engineering humans?
If design has been ongoing, how were they accomplishing all this? Did they spontaneously engineer brand new species out of thin air? Did they take existing species and re-engineer them, inserting bits of DNA as they went?
Is there evidence of such things happening today? Are there brand new species being created at this very moment? Can we find evidence of a designer making new things in nature?
Of course the ID literature is maddeningly silent on this. They seem content to make what amount to little more than grandiose arguments from incredulity when arguing for design. As I re-aquaint myself with ID literature, I am reminded that the entire argument boils down to
"X is complex, we don't know how X evolved, therefore DesignerDidIt".
Yet there is absolutely nothing to be found on where, when and how the designer did any designing. In effect, it explains absolutely nothing.