Scientists accept a theory when the evidence supports it and it explains what we observe. When two theories compete, the one with more evidence behind it is preferred.
The Big Bang theory and the Steady State theory can both explain red-shift, because both say the Universe is expanding. However, only the Big Bang theory can explain the cosmic microwave background (CMB) radiation. The Steady State theory has no reason for a universe that has always looked the same to be filled with leftover radiation from an early hot stage.
There is therefore more evidence for the Big Bang theory than for the Steady State theory. For this reason the Big Bang theory is the currently accepted model for the origin of the Universe. Accepted does not mean proved for ever: if new evidence appeared that the Big Bang theory could not explain, the accepted model could be revised.