Without going into a lengthy analysis... you can infer AoA from groundspeed, rate of climb/descent, pitch/yaw/roll, and position feedback of control surfaces. Recent information on these data points can be used to calculate present and near future flight dynamics. The fields of Kalman filtering, adaptive control, and optimal control as applied to aerospace engineering are decades old.

There are many examples where adaptive flight controls can fly an aircraft that has inherently unstable flight dynamics... In fact most modern jet fighter require computer controlled flight controls to maintain stable flight.

Applying these algorithms to an airliner for sensor truth'ing is a cake walk.

* I think you actually can infer situational AoA from ground speed and altitude data: An example you could build a regression model of standard take-off scenarios and using recent groundspeed, altitude change, and the rate of change of (groundspeed/altitude). You could build this off of flight test data and simulation. In practice, there may be no point to doing this because a wealth of additional flight sensor information is available.