1. Red-shift, which is basically the Doppler Effect, but with light. Because stars in other galaxies appear to give off red light, this shows that they are moving away from us (Earth). Red light is on the far left of the Visible Light Spectrum, so things moving away from us appear to be red, while things moving towards us appear blue (the other end of the spectrum). This suggests that the universe is expanding all the time - and therefore it might have started from a single explosion - the Big Bang.
2. Cosmic Microwave Background Radiation (CMBR) has been found by scientists to be coming from all directions in space, and is suspected to be 'left over' energy from the Big Bang.