the baryon asymmetry
Every time we make a particle of matter in the laboratory, an antiparticle appears alongside it, and when the two meet they annihilate into light. So the natural expectation is a universe born with equal matter and antimatter, which should have annihilated almost completely, leaving nothing but radiation. Yet here we are: stars, planets, and people, all made of matter, with essentially no antimatter anywhere. Why does anything material exist at all? That is the baryon asymmetry problem.
Baryons are particles made of three quarks, protons and neutrons chief among them. The observed asymmetry is tiny but decisive, measured by the baryon-to-photon ratio eta = (n_baryon - n_antibaryon) / n_photon, which is about 6 x 10^-10. In words: in the early universe, for every billion antiquarks there were about a billion-and-one quarks; the billion pairs annihilated into the photons that became the CMB, and the leftover one-in-a-billion is all the ordinary matter that exists today. Generating this excess dynamically is called baryogenesis, and Andrei Sakharov showed in 1967 it requires three conditions: violation of baryon number, violation of both C and CP symmetry, and a departure from thermal equilibrium.
This is a genuine unsolved problem. The Standard Model contains all three Sakharov ingredients in principle, but the CP violation it provides is far too small, and its other mechanisms too weak, to produce the observed eta. So the matter excess is evidence that physics beyond the Standard Model must exist, whether in grand unified theories, new sources of CP violation, or the physics of neutrinos (leptogenesis). We owe our very existence to an asymmetry we cannot yet explain.
If matter and antimatter had been exactly equal, annihilation would have left about one surviving baryon for every 10^18 photons; instead we observe about one for every 1.6 x 10^9. That thousand-million-fold surplus of survivors is the entire material content of the universe, including everything you have ever touched.
One extra quark per billion: the tiny surplus that became all matter.
The Standard Model provides CP violation but far too little to explain the observed asymmetry, so baryogenesis is direct evidence for new physics. Sakharov's three conditions are necessary requirements, not a specific mechanism; which mechanism nature actually used remains unknown.