Friedrich Adolf was born in Lauterbach, Hesse, into a family of the minor German nobility (Riedesel), the second son of Johann Wilhelm Riedesel, Freiherr zu Eisenbach (1705-1782) and Sophia von Borcke (1705-1769).
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There he was cared for by the von Massow family and nursed by their daughter Charlotte.
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In 1781, Quebec governor Frederick Haldimand named Riedesel officer in charge of the Sorel District, where he and his family stayed until his departure from North America at the end of Summer 1784.
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Baum served under Major General Friedrich Adolf Riedesel commanding the Dragoon Regiment Prinz Ludwig in support of General John Burgoyne's 1777 campaign to attack the Lake Champlain-Hudson River corridor, which ended in Burgoyne's surrender at Saratoga on October 15, 1777.
In 1826, he married Perses Narina Tunnicliff, daughter of William Tunnicliff, and granddaughter of the Count George Ernst August von Ranzau, an officer on the staff of the Friedrich Adolf Riedesel, and author of the interesting Journal of Burgoyne's Expedition contained in the archives of the general staff at Berlin.