I am fairly certain the mass of a satellite cannot be determined from the characteristics of its orbit.
We used to have telescopes that tracked and allowed real-time imaging of NEO stuff.
I think it was Teal Blue and Teal Amber, if memory serves, but not sure.
I hope we still have something at least that good. Should be a whole lot better.
If the thrust of the launch vehicle is known and used as a function of orbital insertion velocity and the orbital altitude is known then the mass can certainly be calculated to a close approximation.