As mentioned in this post,
が started as an attributive case particle, became a subject particle, and then turned into a conjunctive particle.
and in modern Japanese it has its main uses as both a conjunctive particle and a subject marker.
While the answer in that question covers its evolution from an attributive particle to a subject particle, how did the use as a conjunctive particle arise? If anything, I would expect "wa" to have evolved as the conjunctive particle instead of "ga" since it already plays a role in contrastive nuance.