Radioactivity was discovered in 1896 by French physicist Henri Becquerel.
And there are now good reasons for thinking that it might have been quite intense in the past, in which case the craters do not indicate an old age at all (see below).
The United States Geological Survey(USGS) website has a lot of indepth material about how the age of the Solar System was determined.
The basics of it are that all material radioactively decays into a stable isotope.
Nevertheless, there is substantial evidence that the Earth and the other bodies of the Solar System are 4.5-4.6 billion years old, and that the Milky Way Galaxy and the Universe are older still.
The principal evidence for the antiquity of Earth and its cosmic surroundings is: Spontaneous breakdown or decay of atomic nuclei, termed radioactive decay, is the basis for all radiometric dating methods.
Fighting the expansion of the Universe itself, the light has had its wavelength stretched out until it gets to us in the form of microwaves.