There is no scriptural evidence for the age of Mary or Jesus. We speculate that Jesus was about 36 when crucified based on scriptural references to the reign of Augustus (31 BC-14 AD) because we can correlate events in Jesus’ life with actual historical events in Augustus’s (Octavian’s)reign, e.g. the census, taxation, and the fact that scripture actually mentions that Jesus was born during his rule. By the way, there are a multitude of “traditions,” some of which are utterly absurd and apocryphal. We need only take a quick glance at the Gnostic “gospels” and other such fictions. Also, the only reference in scripture to Mary is that she was “parthenos” which can mean “young woman” or “virgin”. Actually they are in reality synonymous because any young woman who wasn’t a virgin in first century Judaism would have been summarily stoned to death. As surprising as it seems, because of the failure of scholars to correlate scriptural dates with those revised and updated according to astronimical and scientific refinements of time, Jesus was actually born in 4 BC!
You are mostly right except that there is no contemporaneus evidence that Jesus even existed.