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Jelly, 7 bytes

ẆŒPi\ƇḢ

Try it online!

-1 byte thanks to Unrelated String

ẆŒPi\ƇḢ Main Link
 Ḣ Find the first
Ẇ slice (ordered by length)
 Ƈ where
 i the right list's index is truthy (occurs in)
 ŒP the powerset (stable ordered)

1-indexing saves me a byte, thank you Dennis!