There is another possibility that hasn’t been mentioned- water in the bottom of the fuel tankf. If just the right amount of water gets into the tank, it will allow a mixture of fuel and water to get into the carburetor. And you get the same symptoms. After trying several times to start the engine *some* fuel will make it into the engine from all the shaking as you pull the starter cord. It can be enough to start, and run for a few seconds before more water is pulled into the carburetor and the engine stalls again.
Solution- disconnect the fuel line from the carburetor and let the fuel drain into a clear container. You will see the water in its own layer at the bottom of the container. Don’t forget to drain the fuel bowl on the carburetor also.