GA safety pilot reported a NMAC just after takeoff from a non-towered airport. As the reporters aircraft was climbing out; another aircraft on final conducted a go-around and both aircraft were separated by 50 feet in the departure leg for the same runway.

Narrative

Busy VFR day at WVI; landing and departing Runway 20; uncontrolled. I was acting as a Safety Pilot for a friend for some practice approaches. We were lining up to Runway 20 after a departure with knowledge of an Aircraft Z on a left base. We delayed our takeoff roll; announced a left crosswind departure and Aircraft Z ended up announcing a go-around due to us being on the runway. As we rotated about 50 ft. above the ground; Aircraft Z overflew us by about 50 ft. then made a left turn. Out of reaction; we adjusted our pitch up and it was particularly dangerous in that critical climbout phase with gear/flaps in the transition to be pulled up; thus lost of lift. Although we had right of way in that situation; it was a better decision to reject the takeoff or announce a delayed takeoff. Aircraft Z should've went around with a slight offset to the right. Complacency and the inaction on our part to efficiently use the runway; but there's a slight chance the Aircraft Z was flying fast in.On the return leg we were entering a 45 for a left downwind 20. Aircraft Y was inbound over the city of Gilroy on a straight in to 20. It was an easy decision but we followed them in without a factor; but it required a lot of coordination over the radio of who was following who when Aircraft Y should've flown the standard pattern entry to follow us in.