This is one of those benefit of hindsight things that's always kind of funny to read, since people champion Album X or Album Y as being "the first" when the truth is, back then, critics and fans alike were still looking for a way to define this new genre. Retroactively, it became progressive rock, but at the time? Some people called it prog, some people called it art rock, and I can tell you that it's highly unlikely they called Crimson King prog when it came out. To properly answer this question, you have to agree on what MAKES prog. I see the Moody Blues and the Beatles as being influences on what became prog, but I don't see them as making prog albums. I think you could argue, convincingly, that in terms of what prog BECAME, The Nice was the first true prog band, but In The Court Of The Crimson King is the album where the subgenre began to gain commercial acceptance. But the evolution of music is such that it's really hard to pinpoint the exact moment a genre came into existence as it's happening. You can really only do that backwards, and even then, it depends on how knowledgeable you are about the music of the period.