If you're asking how do we know there is more matter than antimatter in the universe the answer is that it is consistent with the observations/calculations surrounding Big Bang nucleosynthesis and CMB anisotropies. If you're asking what do we theorize is the reason there is more matter than antimatter in the universe there isn't a satisfactory answer yet. It's one of the biggest open problems in physics.

If there were more antimatter than theorized, we'd expect to see much more radiation due to matter-antimatter annihilation. If we don't see this, then there must be a heavy bias in one direction or the other.