Organized matter is real evidence. From it we can safely say, "I infer." That is a proper expression for science, and it holds true for every observer. Unless you mean something more tangible as "real evidence."
Do you observe a play under the assumption you simply don't know if there is a director? Do you expect the director to step onto the stage at every moment to assure you he has a hand in the play? It is certainly possible there is no director. The actors may be ad libbing their lines and have no theme or purpose. But it is hardly unreasonable to assert inductively, or infer deductively, that the director is there yet remaining in the background precisely because that is his role by nature.
One mode of radioactivity is beta decay in which a neutral neutron is converted to a positively charged proton, a negatively charged electron and a neutrino. That is a big change in properties.
I am not familiar with the process you describe. I assume it occurs at a quantum level, it occurs within a certain range of elemental substance, and it serves a purpose without which life on this planet may be very different, if present at all. Perhaps you could explain how we know for certain whether this process occurs erratically in every case, and whether it does not behave accordingto predictable laws.
You can read about beta decay here and about many other radioactive decay modes from the links there. From that page I also learned that there are other kinds of decay called beta decay different from the one I cited (although I think that one is the earliest figured out).
I don't think beta decay per se is essential or influential for life. The main effect is to transmute an atom of one element to the one with a different atomic number. That is, it changes the chemical properties of the atom. If you scroll down in that article you'll see that beta decay turns an isotope of Cesium to an isotope of Barium.
Some radioactive decays are important to us. Fission of uranium is harnessed in nuclear reactors and bombs. Neither may have been important for the devolpment of life but certainly are important to us now. Fission transmutes an atom of uranium into two or more much smaller atoms and some spare neutrons and EM radiation.
Our best explanation for this and other quantum processes is that a system in a given quantum state has a propensity to change in certain ways. An individual system in that state is unpredictable but en masses you can make statistical predictions. For example, in a significant mass of radium 228, half will have beta decayed to actinium in a little less than seven years.
However, I don't think you addressed the implications of these facts for your statement that
The best evidence to falsify intelligent design would be the disintegration of particle matter.