No. She seems him in the airport as a little boy (and for that part, the caster exceeded himself, finding a child who sort of resembles Bruce Willis), as she is kneeling over his adult body, recently slain by a policeman's bullet.
Cole grows up, and then goes back in time, and meets Railly. But since it was a traumatic experience, she can't fully remember where she's seen him before (a typical defense mechanism every psychiatrist knows about). That, and he's grown up.
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