Racing car aerodynamics really started with the 1923 Voisin C6 Laboratoire. There had been earlier attempts at slipstreamers for Brooklands and similar tracks but the designers did not understand what was needed. Gabriel Voisin was also an aircraft designer and for the C6 he created a body form with low drag and low front end lift. The car was not successful alas and forgotten by too many.
The Rumpler-designed Teardrop Benz (1921) is an impressive slipstreamer design. Rumpler and other engineers had to consider engine cooling for an aerodynamic car participating in long races.
Speed record cars had adopted aerodynamics long before GP cars. Speed record cars since La Jamais Conente had been slippery, applied brute force or a combination of the two. The bodies of the Mercedes-Benz and Auto Union speed record cars of the 1930s were designed by engineers striving to manage aerodynamic stability. It is argued that Auto Union attempted to provide negative lift -- a type of ground effect -- in the car in which Bernd Rosemeyer died. In hind sight, it seems strange that M-B and Auto Union applied so little aerodynamic thinking to GP cars at the time.
After WWII and racing engineers being exposed to war planes, aerodynamic thinking was reapplied to GP and sports racing cars simultaneously. Mercedes-Benz made sports racers for long high speed events and, initially, slipstreamers for GP racing. Minimising front end lift was an important consideration in the designs. Who else made GP slipstreamers? Lots of teams, including tiddlers like Connaught. For sports car racing -- or perhaps the desire to win Le Mans -- Jaguar created a compromise design with the C Type; it wasn't really a road car but it looked like one. To get the aerodynamics right, Jaguar had to make the D Type which wasn't a practical road car.
BRM had money to spend in the 1950s and they commissioned aerodynamic studies for the front end of GP cars (if anyone is reading the relevant BRM history volume, please chip in). As I remember, the consultants recommended a new nose cone to reduce (you guessed it) front end lift.
The May brothers may have used a wing on a sports racer in 1955 but that event is even more lost in history than the Voisin C6.
The next serious aerodynamic creation was the nose flap, a flat rigid projection at the front of a car at an upward angle to the road. It matters because it was intended to create downforce -- the first time since Voisin and Auto Union that anyone had a go at it. And a flap was so easy to implement. Even if it didn't work, it looked sexy in the sales brochure.