Quantization effects due to topological invariants such as Chern numbers have become very relevant in many systems, yet, key quantities as the quantum geometric tensor providing local information about quantum states remain experimentally difficult to access. Recently, it has been shown that multiterminal Josephson junctions constitute an ideal platform to synthesize topological systems in a controlled manner. We theoretically study properties of Andreev states in topological Josephson matter and demonstrate that the quantum geometric tensor of Andreev states can be extracted from the absorption of synthetic linearly or circularly polarized microwaves. The integrated absorption provides direct evidence of topological quantum properties of the Andreev states.