The definition of Classic Car is older than 25 years. 25 years ago was 1982. Cars were made on the assembly line since Model T in early 1900s. When I drive my Mercedes 1959 I enjoy the looks. It is a classic as is my 1971 which is my everyday car.
There are a few hand built cars such as the Morgan, Rolls were,
Stutz, and some were you buy the chasis and build the rest.

There were afew classic cars made on a basic production line,depending upon what you classify as ” Classic “,however, most were done by much handcraft work. Often a chassis and engine were specified and then the body type and specifications were done by a body maker and fitted to the chassis. Rolls Royce of course did that, but so did Cadillac, Lincoln, Packard and numerous other companies (especially on into the1920′s and 1930′s).

Since some weasel named Ford invented the “assembly line”, yes they was. But not before.

yes, maybe not as advanced with robots, but they just used people to put things together and build the cars.
Henry Ford started using assembly lines a couple of years after they came out with the first car.

all cars except a few hand built ones of europe were made on an assembly line since the time of Henry Ford who started the process.