Any question about perception - "being seen" - is going to have more than one answer. There's often no easily identifiable tipping point in changes of perception of something like "legitimacy" or "importance" - the composer W.C. Handy thought the blues were important when he heard them at the turn of the 20th century, and some people still don't think that they're important. Additionally, there are quite a few different sorts of music that get called "blues", not all of which have the 12-bar chord progression, and not all of which sound like John Lee Hooker or B.B. King. Furthermore, the difference between jazz and the blues in the early years of the 20th century was not always as clear as it might seem today; things called "jazz" began to be seen as legitimate/important part of musical history much earlier than the kinds of music that now get described as "blues", but were not always that different.

That said, there's two events, both connected with the producer John Hammond, which clearly show music called "blues" in influential situations demonstrating its importance/legitimacy. The first was John Hammond's From Spirituals To Swing concert in December 1938 at the high-brow New York concert venue Carnegie Hall. Hammond presented the concert as a sort of history of African-American music at a point when swing music was very popular, with the aim of showing the genesis of swing music. He included a variety of musicians who played a variety of different forms of blues; famously, according to books like Elijah Wald's Escaping The Delta, Hammond wanted Robert Johnson to play the concert, but Johnson had passed away, likely poisoned, only months earlier. Instead, the concert programme included delta bluesmen like Big Bill Broonzy (who played 'Louise Louise Blues'), boogie-woogie pianists like Meade Lux Lewis (who played 'Honky Tonk Train Blues') and swing big bands like the Count Basie Orchestra (who played 'Swingin' The Blues'). Putting these musicians into the Carnegie Hall setting was, of course, deliberately designed to legitimise them/show their importance to history.

The second was the release of Robert Johnson's King Of The Delta Blues Singers on Columbia records in 1961. Between the Great Depression and the use of shellac (the material that 78rpm records were made from) in the U.S. war effort in World War II, old 78rpm blues records from the 1920s and early 1930s had quickly become very difficult to find by the mid-1940s. Marybeth Hamilton's book In Search Of The Blues points to obsessive collectors in the mid-1940s congregating at the Jazz Record Center in Manhattan as being the setting when old delta blues 78rpm records (like the ones discussed in Amanda Petrusich's book Do Not Sell At Any Price) started to become collectors items that would end up being worth serious money (a clear sign of legitimacy/importance).

Many of these collectors, by the late 1950s and early 1960s, had started to commercially release anthology albums of 1920s-1930s recordings of delta bluesmen. John Hammond, who put on the 1938 concert mentioned earlier, was working at Columbia (a major label record company) in the early 1960s, and he got in on the delta blues anthology trend with King Of The Delta Blues Singers, an anthology album of 1930s Robert Johnson recordings sourced, according to Petrusich, partially through Hammond's own 78rpm collection and that of another collector working at Columbia at the time. At the time, this album (which thanks to the promotional power of a major label, was very often the first delta blues that many young rock & rollers or folkies had heard) made a big impression on people like Bob Dylan, Eric Clapton and the Rolling Stones. Over time, King Of The Delta Blues Singers became seen as one of the major influences on the rock music that would become the dominant popular music of the 1960s and 1970s.

Edit: Reading over this again, I made a mistake: Robert Johnson's recordings weren't from the early 1930s, so I removed the 'early' before '1930s' in the last paragraph.