No momentum at all relative to what? Relativity tells us that there is no fixed frame of reference. In practice what that means is there is no universal zero velocity. You only have velocity relative to other things. The implicit assumption in your argument is that you would have no momentum relative to the earth, which in itself is problematic. After all, the earth spins at a rate of 360 degrees per day, so not moving relative to the earth would mean moving 463.83 m/s relative to the surface of the earth at the equator, which is supersonic. But maybe you mean relative to the surface of the earth. What if you go to the moon? Or mars? Or into orbit? Maybe you mean relative to the nearest big thing. If you could somehow teleport from the ground into a plane, would the plane count as the nearest big thing? What about a bus? That’s on the ground, so maybe the nearest big thing would be the ground, if the mass of the thing matters in how the nearest big thing is determined. You can see how this can quickly turn into a mess of rules and special cases.