actually, it goes the other way.
Buick had their own transmission plant manufacturing the Dynaflow from 1947 to 63.
the other GM divisions were using the Hydra-matic as early as 1939.
the "whoops" moment came in 1953 when the GM corp Hydramatic plant burnt to the ground. without an automatic transmission source, GM was scrambling to find a way to finish their production runs for the year ... so you can find Dynaflows in practically any GM division car at the end of the 1953 model year, especially Cadillac.
https://en.wikipedia.org/wiki/Dynaflow
https://en.wikipedia.org/wiki/Hydramatic
other than that, 1964 ( by which time all production Nailheads were either 401ci or 425ci ) and the "Super Turbine 400" ( which is really just a TH-400 with a switch pitch torque convertor ) would be the earliest appearance of a 'real' Hydramatic in a Buick car.
you'll notice that there was a major Dynaflow redesign for the first year of the Nailhead engine in 1953. 322ci production was from 1953-56, the 264ci wasn't produced that long.
https://en.wikipedia.org/wiki/Buick_V8_engine
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