This work proposes an observational test of the fuzzball paradigm in string theory, which replaces black hole horizons with horizonless microstate geometries. A fixed compactification modulus, previously derived from moduli stabilization in Type IIB string theory, determines the string length and near-horizon structure. This yields a precise prediction for the delay and frequency of gravitational wave echoes from supermassive black holes. The predicted signal falls within the Laser Interferometer Space Antenna sensitivity range, offering a falsifiable, parameter-constrained signature of string-theoretic microstructure.