No, you cannot make an egg omelette with just one egg. Traditionally, an omelette is made by beating multiple eggs together, typically two or more, along with a little milk or water. This mixture is then seasoned and cooked in a pan with some oil or butter.
If you only have one egg, you might be able to make a small scrambled egg instead. Simply crack the egg into a bowl, whisk it with a fork, season it with salt and pepper or other desired seasonings, and cook it in a pan with some oil or butter. However, it won't have the same consistency or structure as an omelette, which is typically made with multiple eggs.