After being rescued by Barry, he and Kara end up in a field outside the city where they introduce themselves in episode 1x18 "Worlds Finest".
The DEO tests Supergirl's abilities in the middle of the desert in episode 1x02 "Stronger Together". Supergirl is tested against the military's Red Tornado in episode 1x06 "Red Faced".
Source: IMDb
Source: IMDb
Source: IMDb