The date of the Moon-forming impact places an important constraint on Earth's origin. Lunar age estimates range from about 30 Myr to 200 Myr after Solar System formation. Central to this age debate is the greater abundance of 182W inferred for the silicate Moon than for the bulk silicate Earth. This compositional difference has been explained as a vestige of less late accretion to the Moon than to the Earth after core formation. Here we present high-precision trace element composition data from inductively coupled plasma mass spectrometry for a wide range of lunar samples. Our measurements show that the Hf/W ratio of the silicate Moon is higher than that of the bulk silicate Earth. By combining these data with experimentally derived partition coefficients, we found that the 182W excess in lunar samples can be explained by the decay of the now extinct 182Hf to 182W. 182Hf was only extant for the first 60 Myr after the Solar System formation. We conclude that the Moon formed early, approximately 50 Myr after the Solar System, and that the excess 182W of the silicate Moon is unrelated to late accretion.