Generally speaking, the Founders had what's known as a "classical education." Their formal education at one of the Colonial Colleges or with a private tutor stressed Greek, Latin, some math including logic and some sciences. The general sentiment of the era was that if one sufficiently trained and prepared one's mind by memorizing knowledge and information, not unlike weightlifting, one could sufficiently pass muster as a gentleman. History, though, wasn't seen as sufficiently challenging. One Harvard student reported that, "The study of history cannot be considered as severe an application of the mind."^1 In effect, it was seen as taking a leisurely stroll while trying to train for a marathon.

This doesn't mean that the men didn't encounter history - as they clearly did. Rather, the Founders that knew what direction they wanted to go in would typically "read" or study the writings or work around that topic which you can see in Jefferson's library. So a young man who was interested in politics or governance might read texts about leaders from the past as a young Jefferson, Franklin, and others did. This goes into the college admission process around that time and provides more information about the content of the coursework.

History didn't fully come into its own as a discipline worthy of study until the late 1800's. (A history of history class from a previous answer.)

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^1 The quote is from Wright, C. E. (2005). Revolutionary generation: Harvard men and the consequences of independence. and I suspect, given your question, you'd enjoy it. It's an in-depth look at the experiences of the men who attended Harvard and the footnotes are full of great finds and resources.