We propose schemes for unambiguous direct observation of Anderson orthogonality catastrophe (AOC) effects in a quantum dot coupled to a charge detector, enabling experimental estimation of the AOC exponent $\alpha$. We show that certain easy-to-measure observables have a robust dependence on $\alpha$ in the non-equilibrium regimes of source-drain voltage bias or thermal imbalance. Our results are obtained using a rate equation formalism in which the AOC effects on tunnel rates are incorporated in an exact manner, and directly support recent experimental results.