'First-born' is a term in Jewish tradition. The first-born is the first male born. The first-born has status of principal heir and successor of his father as head of the family. It does not refer to the order of birth of children, only male children. If I was Jewish, the fifth child, with four older sisters, I would still be the first-born.
Luke was a Gentile...He wasn't repeating Jewish tradition...He is telling a story from a Gentile point of view...As here for example:
Luk_1:9 According to the custom of the priest's office, his lot was to burn incense when he went into the temple of the Lord.
When something was a custom or a tradition, Luke mentioned it...Luke, as a Gentile called Jesus the firstborn because he knew that Jesus had younger brothers and sisters...
I probably shouldn’t stick my nose in at this point, but if assume Luke was Greek, shouldn’t we also assume he was familiar with the Greek traditions relative to primogeniture?
You are just making that up. Show me that in Scripture.