Quem escreveu a música para a primeira cena do Star Wars?

As músicas em questão, "Cantina Band 1 & 2", foram escritas por John Williams e tocadas pela London Symphony Orchestra.
Williams foi o compositor de todas as faixas no filme.

Acho que este é o que você está procurando:

Isto é feito pelos artistas: Figrin D'an e os Nós Modais

No universo, agora temos a confirmação canônica do Not For Nothing que a música era composição original do compositor Bith e bandleader Figrin D'an e tocou na cantina por sua banda, Figrin D'an e os Nós Modais .

The reason should be obvious: Figrin D’an is the best composer and bandleader you will ever find this side of the galaxy. We knew that if we left, we’d never be able to find another leader quite like him. When we’re getting thrown into shackles or washing sand out of our eyes, it’s hard to appreciate him. When we’re playing, nothing in all the worlds is better.

...

As we played another one of D’an’s newest songs (captivity had been strangely inspirational to him, I have to admit), I thought about those droids and the stormtroopers that searched for them. I thought about a possible reward. And then I decided that if that human could do us a favor without us knowing him at all, we could do those other humans a favor and not report them. We were safe now, and could keep playing.

_{^{From a Certain Point of View: Not for Nothing}}