First couple seasons of TNG were pretty rough. If someone told me the first episode of something I should love was "Encounter at Farpoint", I think I'd drop the show after the first episode.
I'm going to suggest something different: Enterprise Season 1 Episode 1.
A new watcher would be on nearly equal footing with the crew in discovering the galaxy beyond Earth. Many of the same frustrations about being held back or being naively altruistic would be genuine human responses new viewers could identify with.