The Great American Dream Machine is now 35 years old and improving with age.

Students of ancient history might be interested in learning that in 1953 the first production Corvette was assembled in Flint, Mich. All total, 300 fiberglass-bodied roadsters were built, all in Polo White and all powered by the ''Blue Flame Six,'' a fancy name for Chevy's in-line six-cylinder engine, better known as the ''Stovebolt Six.''

From its rather primitive beginning (even by sports car standards of 1953), the Corvette became a decent sports car, a good sports car and today, perhaps even a great sports car. Of course, there are a handful of very expensive exotics that can out perform it, but these are the cars of auto enthusiast magazine articles, photographs, movies and television and the imagination. Very few will be seen on the road.

The Corvette, on the other hand, can be seen everywhere. With more than 900,000 of them built in the past 35 years with a fairly decent rate of survival, one is bound to see several - old, new and in between - on any trip. And they all look good. The bright red convertible test car, though, could have been the fairest of them all.

Here was a car that turned heads, brought cheers from young boys, caused looks of admiration from teen-agers of both sexes, produced thoughtful looks from adults and, in general, brightened up the scenery. Even those who pretended they weren't impressed - mostly older men in expensive European cars and young nerds in economy cars - weren't quite as blase as they tried to appear. They managed to sneak in some glances while trying to look nonchalant.

But aside from superior handling and performance, looks aren't skin deep in a Corvette. They are part of the Corvette mystique. In other words, it not only has to run good, it has to look good.

A new Corvette convertible is, obviously, not within the reach of the average car buyer; or even the above average car buyer. The test car at almost $39,000 is not likely to be the biggest priority to most people. But for those who have arrived, it certainly presents a way to arrive in style.

Who, though, is the average Corvette buyer? Really anyone with the money. But a Chevy demographic study notes the average age is 40, 84 percent of all buyers are men and the median income is $83,000. So, you may say it is a car for well-to-do old men; that is if you are viewing all of this from an age far below 40. Age and money certainly go a long way in owning a Corvette, not only in being able to purchase it but being able to afford the insurance.

A Corvette owner must be in the position to call up his/her insurance agent and say, ''Hey, put my new Corvette on the policy.'' As with J.P. Morgan's comment on the price of a yacht, if you have to ask, you can't afford the insurance on a Vette.

But enough of these mundane matters, let's jump in the Vette and get away.

First off, though, jumping in a Vette is not as easy as it may sound. It takes a bit of agility, a bit of finesse and a bit of imagination. It is actually projecting one's self through a narrow opening, over a high sill into a confined area. This is the easy part, getting out is what really puts a person to the test.

All of this, fortunately, is easier when the convertible top is down; bringing us to our next subject - raising and lowering the top. There is a set of instructions on this subject, which look very complicated but the task proves to be very easy and can be learned very quickly, especially by those who were born before the computer and video age. Those raised on Erector and Tinker Toy sets will have a definite advantage.

Once seated in and strapped up, the next step is to start the engine - a 350-cubic-inch/5.7-liter V-8 rated at 245 horsepower at 4,300 rpm and 340 foot pounds torque at 3,200 rpm. The engine is really an update of the Chevy 350 V- 8, which has been around for a number of years and in this version features aluminum heads and tuned-port fuel-injection. The 350 V-8 is one of the few survivors of the Golden Age of the American overhead valve, short stroke V-8 engine; an engine of incredible durability, amazing performance and relatively low cost. (Back in the late '60s and early '70s, the American factory performance or muscle car could outrun - at least in a straight line - just about anything in the world, and at a fraction of the cost.)

Turn the key and the V-8 rumbles to life. Although this may sound as somewhat of a cliche, V-8s actually do rumble and more so with dual exhaust and four pipes sticking out the back. A glance at the electronic instrument panel may at first be a little intimidating but it proves to be easy-to-read and easy-to-interpret. The speedometer and tachometer, for example, are done up in both analog bar graphs and digital readouts. The engine function instruments also have readouts. Controls are not in the least bit complicated. In fact, this state-of-the-art car still has the old-fashioned-type push-pull headlight switch on the upper left side of the dash.

The test car had the ''4-plus-3'' manual transmission. This is a sophisticated unit that, as the name implies, is a four-speed transmission plus overdrive in second, third and fourth. What this really does is add a fifth gear on top and allow ''splitting'' gears between second-third, third- fourth and fourth-fifth (overdrive). The split and fifth gear are activated by a button on top of the shifting knob.

The transmission is not the most difficult one to master but definitely not one to learn on. Clutch pressure is fairly strong and it does take some effort. Again, not out of sight but it is not a stabber and grabber. So, place it in low, release the clutch and you are off. Not enough gas and it will stall, too much and it will spin those big Goodyear EagleP275/40ZR-17 unidirectional tires (part of the Z52 optional suspension package). And if you really go wild on the gas, there's a good chance that the whole back end will spin out as the 350 V-8 releases all that low end torque. But play it cool and you are on your way, happily shifting.

The next thing one will notice is that the Corvette will go where you steer it, and very fast at that. Obviously not a car for those who do not like to pay attention to their driving. The sophisticated four-wheel independent suspension is tuned for fast, flat maneuvering. Least we forget, this is a sports car and it handles like one. So, depending on your level of driving skill and your driving aspirations, the driver will either ride in the Vette or drive the Vette.

Although most of the joy of driving the Corvette is taken away by law, most notably the 55-mile-an-hour speed limit, it will be a matter of pride knowing what the car is capable of doing. According to Chevy figure s, this comes out to 0-60 mph in 5.3 seconds, the quarter-mile in 14.21 seconds at 97.2 mph and a top speed or 155.4 mph. (The automatic version is only a fraction slower.)

One of the big surprises of the Corvette is that fuel mileage is not really bad. In fact it is pretty good, though not if one is traveling at the above mentioned speeds. EPA rates the four-speed manual version at 17 mpg city/24 mpg highway. The test car, driven as most Corvettes will probably be driven, achieved 13 miles per gallon for city driving and 22 for highway driving. Unleaded premium must be used.

The Corvette is covered by a 12-month/12,000-mile warranty on the entire vehicle; a 6-year/60,000-mile power train warranty and 6-year/100,000-mil e outer-body rust-through warranty (since the car is fiberglass, it is doubtful if the rust-through protection will be needed).