Goetz, the son of a salesman, came into contact with music early in his life. However, he did not receive his first serious piano lesson until 1857 – although he already had begun to compose some years before. At the end of the 1850s, he began to study for a degree in mathematics, but broke this off after three terms to study at the Stern Conservatory in Berlin, where he studied piano and composition with Hans von Bülow. In 1862 he graduated from the conservatory.