I guess that they referred to the scriptures that became known as "The Old Testament". As in the case of the Berreans and many others.
As to how they substiancianted their claims about the deeds of Christ - who knows? Maybe the miracles and word of mouth meant that they story spread on it's own among believers and non believers alike.
Without looking it up, I believe that several people at the time who were not believers wrote about the works and miracles of Jesus.
Any help ?