Bold guess:
はじめて書くMeans to compose, rather than just write. “to write for the first time”
Anyone can copy and 書くa masterpiece that has already been composed.
I think, in line with what Heiopei said, this is the “originate” meaning of はじめる, or “was first written” as in “The song was first/originally written by a love struck courtesan”
normally the て-Form of a Verb + はじめて means something like “only after” or “not until”. My guess the sentence means something along the lines of: “This song is a work that could only be written after becoming a genius like Beethoven.”