So, then the elements are created by experiment with the belief that they would exist anyway. Or maybe they exist in great numbers if right the conditions exist, for example: they exist in a super nova, etc.? Or maybe during the formation of a black hole?
Actually seeing the very heavy elements, however fleetingly, in a lab is important. If you look at this chart the number of protons (Z) goes down the right hand diagonal, while the number of neutrons (n) goes down the left hand diagonal. The most stable isotopes are in the center of the chart as you move diagonally. What you will notice is that for the lighter elements, the number of protons and neutrons is roughly the same (12C has six of each, oxygen's most stable isotope has eight of each.) But as you go further down the chart, you discover that the heavier an atom gets, the more the number of neutrons increases relative to the number of protons.
The reason for this is that the protons and neutrons are attracted to each other via the strong nuclear force, but protons also tend to repel each other because of their electric charge. To balance the strong force against the electromagnetic force, the electrically neutral neutrons provide a "screening" effect where they shield the protons from each other. This effect requires more and more neutrons to keep the nucleus stable as the number of protons increases.
With this simple model, maybe elements of arbitrarily large atomic mass can exist. But maybe they can't. We do not know the orbital structure of nucleons anywhere near as completely as we know the orbital structure to be for electrons [for Hydrogen, electronic orbital configuration is an exactly solvable problem, and for heavier elements it's a multibody force problem, which can't be solved in closed form, but the computer models are very good --for electrons.] Because of this, it's quite possible that nature might reach a point where no amount of neutron shielding can keep the protons close enough together to keep an atomic nucleus stable.