Upcoming LIGO/Virgo/KAGRA (LVK) observing runs promise to detect a variety of inspiralling gravitational wave (GW) events, which come from black hole and neutron star binaries. However, all non-inspiral GW sources remain firmly out of reach for the next decade. We report the discovery of a new non-inspiral GW source class, which is the first that might be detectable by LVK run A+, or the Cosmic Explorer. Some dying massive stars launch bipolar relativistic jets, which inflate a turbulent energetic bubble -- cocoon -- inside of the star. We simulate such a system using state-of-the-art 3D general-relativistic magnetohydrodynamic simulations and show that cocoons emit quasi-spherical GW emission in the LVK band, 10-100 Hz, over a characteristic jet activity timescale, 10-100 seconds. These GWs from jetted stellar explosions are expected to be detectable multi-messenger sources as they will be accompanied by electromagnetic emission from the energetic core-collapse supernova and cocoon.