First time Cadillac introduced......?

[The Tassie Devil(le)]

Probably with the Cimmaron?

Bruce.

[Jay Friedman]

The last Cadillac 3-speed manual transmission until Hydramatic became standard equipment in 1954 was synchronized in 2nd and 3rd gears only, as were all other US car transmissions of that era I'm familiar with.  The next Cadillacs offered with a manual gearbox, the Cimarron, must have had a fully synchronized 4-speed transmission, as did most US cars by the '80s, but I'm not sure.  The CTS, the next Cadillac offered with a manual transmission, the 2002 CTS did have a fully synchronized transmission.