Help with this 「見てきたい」 expression.

Example:
“I want to see you grow up. 見てきたい！”

Help with:
見てきたい = I expect to see it (you grow up) (future tense, with a sense of hope)

Does that sound about right?

More background on this if needed below:
I’ve been watching Japanese movies w/no subs and putting my listening skills to work. I heard a man tell his daughter the above sentence followed by that expression 「見てきたい」. And that is what I took away from it.