Why do so many people refer to the 'big bang' theory as fact?

The night sky presents the viewer with a picture of a calm and unchanging Universe. So the 1929 discovery by Edwin Hubble that the Universe is in fact expanding at enormous speed was revolutionary. Hubble noted that galaxies outside our own Milky Way were all moving away from us, each at a speed proportional to its distance from us. He quickly realized what this meant that there must have been an instant in time (now known to be about 14 billion years ago) when the entire Universe was contained in a single point in space. The Universe must have been born in this single violent event which came to be known as the "Big Bang."

Astronomers combine mathematical models with observations to develop workable theories of how the Universe came to be. The mathematical underpinnings of the Big Bang theory include Albert Einstein's general theory of relativity along with standard theories of fundamental particles. Today NASA spacecraft such as the Hubble Space Telescope and the Spitzer Space Telescope continue Edwin Hubble's work of measuring the expansion of the Universe. One of the goals has long been to decide whether the Universe will expand forever, or whether it will someday stop, turn around, and collapse in a "Big Crunch?"

Background Radiation

According to the theories of physics, if we were to look at the Universe one second after the Big Bang, what we would see is a 10-billion degree sea of neutrons, protons, electrons, anti-electrons (positrons), photons, and neutrinos. Then, as time went on, we would see the Universe cool, the neutrons either decaying into protons and electrons or combining with protons to make deuterium (an isotope of hydrogen). As it continued to cool, it would eventually reach the temperature where electrons combined with nuclei to form neutral atoms. Before this "recombination" occurred, the Universe would have been opaque because the free electrons would have caused light (photons) to scatter the way sunlight scatters from the water droplets in clouds. But when the free electrons were absorbed to form neutral atoms, the Universe suddenly became transparent. Those same photons - the afterglow of the Big Bang known as cosmic background radiation - can be observed today

Ariella has it precisely. Points to her. I'll add to hers though, Hubble upon putting together the thought of an expanding universe went on to use science and math to present to his theory of universal expansion to his fellow scientists. I believe it was Einsteins theory of general relativity that, among other things, predicted that if in fact the "big bang " occurred then there should be a residual glow left over. We didn't have the ability to see or measure this background radiation at that time, so his was a blind prediction (as it were). Only recently have we had the capability to measure the radiation. When it was measured and mapped, Hubble's theory was proven. I am not sure if the theory has been re-proven yet but it should make sense to verify such an outstanding theory.