William Greif was born and raised in Cleveland Ohio with at least three brothers (Charles, Louis and Thomas) who later joined him as business partners in the Greif Brothers Cooperage Co. He was educated in Cleveland schools. He began in the manufacture of kegs and barrels in 1876 (Biographical Dictionary of Living Men of Cleveland, 1914) and was a founder with Albert Vanderwyst (1820s-1882) of the Vanderwyst & Greif Cooperage in 1877 (greif.com). The partnership was apparently cemented with William standing as Godfather to Albert's next child, Charles William Vanderwyst (1877-1952). With Albert's death in 1882 he invited his brothers into partnership in the firm, renaming it Greif Brothers Cooperage Co. and buying out Albert's half of the business from his widow Charity in 1883. The two families remained close, however, as William was mentioned prominently in a notice summarizing his godson's wedding in 1901.
By 1914 William Greif is clearly a pillar of the Cleveland business community. He is listed as the "president of the Greif Bros.' Cooperage Co. and the Fanner Mfg Co.; vice president of Euclid Arcade, Pioneer Lumber Col, and General Time Recorder Co.; treasurer of Columbia Mutual Lumber Col; director in the following companies: Cleveland, ALliance & Mahoning Valley R. R., Forest City Savings & Trust Co., Ohio Savings & Loan Co., United Banking & Savings Co., California Red Wood Lumber Co., and the Stark Electric R. R. Co.; member of the Chamber of Commerce, Chamber of INdustry, and Cleveland Athletic, Clifton, and Lakewood Tennis Clubs (Biographical Dictionary of Living Men of Cleveland, 1914)."