It's all about the audition, not the degree. That said, most people who make it into orchestras have graduate degrees in music performance.
By audition
Bournemouth Symphony Orchestra was created in 1893.
London Symphony Orchestra was created in 1904.
Nuremberg Symphony Orchestra was created in 1946.
Leeds Symphony Orchestra was created in 1890.
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By audition
The first symphony orchestra was in Germany.
Carmel Symphony Orchestra was created in 1976.
Dallas Symphony Orchestra was created in 1900.
Stavanger Symphony Orchestra was created in 1938.
Bern Symphony Orchestra was created in 1877.
Knoxville Symphony Orchestra was created in 1935.
BBC Symphony Orchestra was created in 1930.
Szeged Symphony Orchestra was created in 1969.
Sault Symphony Orchestra was created in 1956.
New Symphony Orchestra was created in 1991.