From what can we conclude that the gas pressure is the same in all directions?

The conclusion that the gas pressure in all directions is transmitted in the same way can be made on the basis of experience. The experiment requires a cylinder with a piston, to which a hollow ball with small holes distributed over the surface is connected. If you fill the cylinder with smoke, and then push it through the ball with a piston, then the same plumes of smoke will be emitted from all the holes in different directions. They are the same because the gas transfers the pressure exerted on it in all directions in the same way. Similar experiments were performed by B. Pascal. He also formulated the appropriate law.