We use a numerical Galactic chemical evolution model and find that the common envelope jets 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 Milky-Way (MW) Galaxy. 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 a 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.