Interpreting Genesis Symbols for the Trinity

Some evangelical preachers claim that Jesus is walking all over the pages of the Old Testament.

The Old Testament, of course, doesn't say so. But believing Christians all the way in antiquity claimed that the Jewish Scriptures not only predict Jesus but also portray him, as a person involved with the creation of the world and the history of Israel.

Where would they get such an idea? And how do they find Jesus as an active figure in the very first book of the Old Testament, from Adam and Eve to the flood of Noah to the story of Joseph, and lots of places in between? Are they just makin' stuff up, or is there a logic behind it all?