Scenario 1:(Your OC Here) wakes up on an outpost a few dozen light-years out of the galaxy.No big deal,although the past would disagree.

Scenario 2:(Your OC Here) was hired to do guard shift for Earth.Not many people lived on the old planet anymore,especially since the Sun should've exploded about 58 years ago.Give or take a few billion.Jupiter was used up for the first ever space-station's fuel supply,so no worrying about getting crushed by that gravity if you head off Earth.

Scenario 3:Start however you want.The universe is quite endless,even now,after all.