You don't know that.
First, you seem to be demanding an "either/or" -- either a designer is responsible for all characteristics and changes, or there is no designer. That's not a serious scientific argument: real scientists are comfortable with systems in which multiple causes can work together. But it is a convenient claim for those who are predisposed to deny the possibility of a designer in the first place. (The reason why they deny the possibility is usually religious in nature...)
Second, while one can spot the signatures of current methods, one need not assume that a designer is constrained to use only those we know about. For example, in Darwin's time selective breeding was the only known method of genetic engineering. They'd never have dreamed that genetic changes could be purposely inserted into a cell to produce insulin -- they'd have been utterly unable to detect it. We can likewise reasonably assume that future advances in genetic engineering will involve methods that are not known to us today. We need not assume that a designer is constrained to operate within the bounds of current technology.
When we step back to your argument as a whole, what you seem to be saying is that a "real" scientist would never even hypothesize "design" in the first place. That's not science, it's merely a bias -- and a supremely ridiculous one at that, given that we already know "design" is at least a valid hypothesis.
There is no possible way to prove that things aren’t designed by an all-powerful (from our point of view) agent.
The question science asks is whether it is possible for living things to be the result of inherited incremental changes. And that’s exactly what genomes look like.
In any question presented to science, the critical question is not whether a phenomenon could be the result of miraculous or extraordinary intervention, but whether it could be the result of ongoing regular processes.