We determined interstellar cosmic ray exposure ages of 40 large presolar silicon carbide grains extracted from the Murchison CM2 meteorite. Our ages, based on cosmogenic Ne-21, range from 3.9 ± 1.6 Ma to ∼3 ± 2 Ga before the start of the Solar System ∼4.6 Ga ago. A majority of the grains have interstellar lifetimes of <300 Ma, which is shorter than theoretical estimates for large grains. These grains condensed in outflows of asymptotic giant branch stars <4.9 Ga ago that possibly formed during an episode of enhanced star formation ∼7 Ga ago. A minority of the grains have ages >1 Ga. Longer lifetimes are expected for large grains. We determined that at least 12 of the analyzed grains were parts of aggregates in the interstellar medium: The large difference in nuclear recoil loss of cosmic ray spallation products 3He and 21Ne enabled us to estimate that the irradiated objects in the interstellar medium were up to 30 times larger than the analyzed grains. Furthermore, we estimate that the majority of the grains acquired the bulk of their cosmogenic nuclides in the interstellar medium and not by exposure to an enhanced particle flux of the early active sun.