Starting on Wednesday, Hamil-fans will be able to enjoy a double dose of America’s newly favorite founding father: a public exhibition of a trove of documents held privately for more than two centuries by descendants of Alexander Hamilton, in a display at Sotheby’s designed by David Korins, the set designer for the musical “Hamilton.”

But one morning last month, many of the documents, which will be auctioned on Jan. 18, were spread on a table in a conference room at Sotheby’s Manhattan headquarters. Joanne Freeman, a historian at Yale and a leading expert on Hamilton, had come to look through them.

Ms. Freeman is a seasoned archive hound, but this was no ordinary day at the office. When Selby Kiffer, an international senior specialist at the auction house, pulled out a simple sheet inside a protective plastic sleeve, she fell into a hush.

“This is one of the most consequential documents in American history,” Mr. Kiffer said, holding up the 1777 commission naming Hamilton, then a promising but obscure military officer, aide-de-camp to Gen. George Washington.