The currently accepted age of the sun is about 4.5 billion years, and is based on a knowledge of the rate of nuclear reactions occuring within it, which affect its density, pressure, temperature, etc.. By knowing the luminosity and temperature of the suns surface, we can estimate its age
Wikipedia: The Sun was formed about 4.57 billion years ago from the collapse of part of a giant molecular cloud that consisted mostly of hydrogen and helium and which probably gave birth to many other stars. According to science.
It's name, as a star, is Sol. Hence, "solar" system.