The Synoptic Gospels tell us God was pleased with Jesus at his baptism. Therefore, any Synoptic claim about what pleases God may serve as implicit testimony about Jesus' life in Nazareth. For example:
In Matthew 6:16-18, Jesus tells us that God rewards those who fast secretly, who put oil on their heads and wash their face, so that no one will know they are fasting. If rewarding such behavior means God likes that behavior, then Matthew must be implying this behavior was characteristic of Jesus before his baptism. We can reconstruct this with a simple inversion of Matthew's statement and say: According to Matthew's direct implication, there were times in Nazareth when Jesus fasted, but he washed his face and put oil on his head so that nobody could tell, except for the Father. And the Father saw Jesus do this, and the Father was pleased by it. (Note: For the moment, we will refrain from interpreting "reward".)
Now, let's consider this argument.
I would contend this is simply the most logical, straightforward implication of Matthew's own testimony. The only required interpretation, assuming God's reward implies God's pleasure, is hardly a stretch. Furthermore, reading this verse as a reflection of Jesus' own life is confirmed by Matthew's narration at the end of the larger passage, in which he says Jesus taught as one having authority.
If this is not valid, we would have to assume that Matthew thought Jesus was inventing new strategies for fasting which he'd never practiced himself. That certainly doesn't seem to fit Matthew's high opinion of Jesus and would actually place him closer to the showy hypocrites just decried in the same series of statements. And Matthew must have an opinion on this one way or the other, unless we suppose Matthew had mentally divorced Jesus' teachings from Jesus as a man. Personally, I do not believe that was the case.
Therefore, if we take the original passage as an historical teaching of Jesus, according to Matthew, then we may also take the inversion of it as a historical aspect of Jesus' life in Nazareth. According to Matthew, by direct implication, there were times in Nazareth when Jesus fasted. This does not tell us how many times Jesus fasted, how often or from what age in life he began doing so, but it does describe characteristic behavior which qualifies as historical activity, and dates to before Jesus' baptism (according to the premise at top).
If this first example is valid, we should keep testing our new methodology. We may also begin to hope that what have been called the Lord's "silent years" may indeed sound forth as echoes, through direct implications of the Synoptic Gospel writers.
To be continued...