Yes, theoretically. But it doesn’t actually get hot enough.
An egg needs a temperature of 158°F to become firm. In order to cook, proteins in the egg must denature (modify), then coagulate, and that won’t happen until the temperature rises enough to start and maintain the process.
The sidewalk presents several challenges to this. According to an experiment reported in Robert Wolke’s book, What Einstein Told His Cook: Kitchen Science Explained, sidewalk temperatures can vary depending on the composition of the sidewalk, whether it is in direct sunlight, and of course, the air temperature. Dark objects absorb more light, so blacktop paving would be hotter than concrete. More often than not, sidewalks are concrete. Wolke found that a hot sidewalk might only get up to 145°F. Once you crack the egg onto the sidewalk, the egg cools the sidewalk slightly. Pavement of any kind is a poor conductor of heat, so lacking an additional heat source from below or from the side, the egg will not cook evenly.
Something closer to the conditions of a frying pan would be the hood of a car. Metal conducts heat better and gets hotter, so people actually have been able to cook an egg on a car hood’s surface.
Still, the idea of cooking an egg on a sidewalk won’t die. It is so intriguing that the city of Oatman, Arizona, hosts an annual Solar Egg Frying Contest on the 4th of July. Contestants get 15 minutes to make an attempt using solar power alone. Oatman judges, however, do allow some aids, such as mirrors, aluminum reflectors, or magnifying glasses, which would help to focus the heat onto the egg itself. It turns out that eggs also have a bit of an advantage in Arizona, the land of low humidity and high heat. Liquids evaporate rapidly when humidity is low. The eggs have a bit of “help” while they cook, and they dry out faster.
I bet you were wondering what is the origin of the saying? It’s not clear, although there is a reference to it in the Los Angeles Times on October 5, 1933, and even as far back as June 11, 1899, in The Atlanta Constitution–so the idea had captured the American imagination and become one of our common sayings by that time. And what about the other saying, “it’s so hot the chickens are laying hard-boiled eggs?” Well, what do you think?