Have we ever found any living organism that doesn't
have genetic material?

Non-cellular life, or acellular life is life that exists without a cellular structure for at least part of its life cycle. ... The primary candidates for non-cellular life are viruses. Some biologists consider viruses to be living organisms, but others do not.

All the self-reproducing cellular organisms on the Earth so far examined have DNA as the genome, and the informational flow from DNA to RNA to protein is the basis of their biological function (Alberts et al. 2008). Based on this fact, almost all the biologists must think that there is no organism without DNA.

the principles and empirical processes of discovery and demonstration considered characteristic of or necessary for scientific investigation, generally involving the observation of phenomena, the formulation of a hypothesis concerning the phenomena, experimentation to test the hypothesis, and development of a conclusion that confirms, rejects, or modifies the hypothesis.