I'm trying to breakdown the tagline for the movie 火垂るの墓 in a movie poster: "4歳と14歳で、生きようと思った"
My first guess was that the で here is the て-form of the copula だ, so it just joins that clause to the next.
But the whole sentence makes more sense if it's the particle で that expresses a cause, as in, "since they were (only) 4 and 14 years old, ...", but it seems like a strange place to put a comma.
The structure [volitional + と思う] here, as I understand from the Dictionary of Basic Japanese Grammar (p.569), indicates the speaker's desire, or what the speaker intends to do.
But I'm not sure how to map that explanation to this sentence.
My best guess here is that the tagline means, "Since they were (only) 4 and 14, I thought that they would live", but I feel like I've misunderstood this sentence.
There are a few other threads about ~おうと思う, but I don't think they answered my question.
Thanks for the help.