We use a numerical Galactic chemical evolution model and find that the common envelope jet supernova (CEJSN) r-process scenario can account for both the very early average ratio of europium to iron and its evolution at later times in the the Milky Way. In the CEJSN scenario a neutron star (NS) spirals in inside a red supergiant (RSG) star all the way to the core and destroys it. According to this scenario r-process isotopes are nucleosynthesized inside neutron-rich jets that the accretion disk around the NS launches inside the core. The merger of an NS with an RSG core already takes place in the very young Galaxy. We conclude that CEJSNe can be a major contributor to r-process nucleosynthesis.