The number of atoms in the universe is not known to be infinte or finite. The biggest problem is that we cannot see all of the universe. The universe is only 13.8 billion years old, meaning that we can only see 13.8 billion light years in any given direction. This portion of the universe, usually called the "observable universe", has been estimated to contain roughly 10122 bits of information and 1080 atoms.
It does not matter what "your current thoughts are" -- beyond those estimates for our corner of the universe, you're guessing.
Atoms can certainly be created or destroyed. A simple example is when a proton (which is a Hydrogen nucleus) meets an antiproton, becoming two gamma-rays. If those gamma rays bug you as "still being something," they can of course be absorbed by an electron in orbit around an atom, ionizing that atom. Another example would be when a proton absorbs an electron, becoming a neutron, or when the Sun fuses hydrogen atoms into helium atoms, which is many-to-one.
It is thought that there is a fundamental symmetry of the universe, which is that the laws of physics are the same from second to second (including, say, the values of the various constants). As a mathematical consequence, there exists a number you can define, which physicists for a lack of a better name call the "energy" of the system, which never changes. For a particle at rest, this number is proportional to that particle's mass, hence you can think that in some sense this number abstracts away what "stuff" really means, as far as the universe is concerned. In that particular sense, "stuff" (in the form of energy) cannot be created or destroyed, unless the laws of physics are time-varying.
We have a very good theory of particle physics which we also happen to know is completely incorrect at its deepest levels, but which has now made extremely accurate predictions and is a shining jewel of modern physics: it is known as the Standard Model. It has several other symmetries which create unchanging numbers which may be of interest to you: momentum, angular momentum, electric charge, color charge, weak isospin, weak hypercharge, baryon number, electron number, muon number, tau number. The most promising ones of these, for your purposes, are the last four: unfortunately, we discovered that these are experimentally incorrect, because they hinge on neutrinos being massless particles, but neutrinos have been discovered to have mass. So even if you start labeling quarks as having existence +1 and antiquarks as having existence -1, so that the overall number of quarks appears to stay approximately constant and your protons can annihilate with antiprotons, there are rare counterexamples involving so-called sphalerons which occasionally lead to the number of quarks increasing by 3 or so, at the cost of the number of leptons (electrons and their ilk) increasing by 3 as well. In some Grand Unified Theories combining the Standard Model with gravity, the number of baryons minus the number of leptons is conserved, but these theories are often a little shaky about what to do with the neutrino mass.