Biological organisms on Earth are proof that there was no designer. Why would an all powerful, all knowing being create life that is feeble, easily killed, depends on the breathing of air and the consumption of other living organisms to live? The human body alone would be a disaster of a design if it were designed.
Just look at the human throat. Air and food, both required to keep the human body alive, go down the same pipe. People die from choking on food. This is one example of how poorly the human body works.
The complexity of something does not equate to intelligent design.