To be fair, we don’t see Jack’s either, there’s definitely implied to be a bunch of stories between TEC/TDD and BT (the 9 Titan comics being set in that gap as well)
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Oh, I’d imagine, but then, a lot of companions first TARDIS trips might not actually be their first…
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Oh, I shall! 
Oh and since @SweetAIBelle listed them all, I think my Ranking would change into this with all onscreen First Trips:
- The Daleks Masterplan
- The Time Warrior
- The Time Meddler
- Remembrance of the Daleks
- Image of the Fendahl
- An Unearthly Child
- The Smugglers
- School Reunion
- The Romans
- The Fires of Pompeii
- State of Decay
- The Ribos Operation
- The Marian Conspiracy
- The Caves of Andorzani
- The Robots of Death
- Beast Below
- The Ark in Space
- The Tomb of the Cybermen
- Mawdryn Undead
- Castrovalva
- The Underwater Menace
- Smile
- The Ark
- The End of the World
- Rosa
- The Long Game
- The Rings of Akhaten
- Colony in Space
- Space Babies
- Planet of Fire
- Sword of Orion
- Terminus
- Vampire of Venice
- The Girl in the Fireplace
- The Dominators
- The Shakespeare Code
I think that’s all (added two of the EU, not sure with most of those but I think the ones I did were probably their first Trip(?)
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