Bright squeezed light has entered strong-field atomic physics, creating an immediate need to characterize the quantum field delivered to the target on subcycle timescales. Here we show that attosecond streaking maps the coherent displacement and phase-sensitive covariance of a displaced squeezed field onto distinct harmonics: the mean photoelectron momentum follows an ω-periodic shift of the spectral center, whereas the momentum variance exhibits a 2ω-periodic breathing. A Feynman–Vernon formulation represents Gaussian quantum light by stochastic vector-potential trajectories, enabling Coulomb-resolved TDSE simulations with a finite XUV gate and without explicit photon-state propagation. A coherent-state reference calibrates the streaking phase and variance background, enabling retrieval of the coherent amplitude and phase together with the squeezed-noise amplitude and squeezing phase. This establishes attosecond streaking as an in situ, gas-phase diagnostic of bright squeezed light.