We construct a testable cosmological model from open quantum gravity: the observable patch is treated as an open system coupled to inaccessible environmental degrees of freedom beyond the apparent horizon. Tracing out the environment in the Schwinger–Keldysh formalism generates a causal influence functional with dissipation and noise kernels, leading to an Einstein–Langevin description. At the homogeneous level, we define the effective coupling by the area derivative of the generalized horizon entropy, G-1eff(H) ≡ G-1 + 4 dSout/dA. After renormalizing the leading area law into G and enforcing early-time GR recovery, the leading infrared contribution in a minimal analytic expansion is dSout/dA ∝ H2⋆/H2, supported by both EFT and microscopic horizon-correlation arguments. The resulting background admits an exact analytic solution H(a) in terms of the Lambert W function and approaches a future de Sitter fixed point without local ghost fields. At the perturbative level, UV recovery, IR matching to Geff(H), causality/passivity, and model minimality motivate a single-pole (Debye) retarded kernel as the baseline benchmark; we also provide the multi-pole extension and ODE localization. Introducing auxiliary polarization variables (X, Ξ) localizes the non-local memory into a manifestly causal ODE system that preserves Bianchi identities by construction and admits regular adiabatic super-horizon initial conditions. We derive observational templates: two-plateau growth suppression with transition scale ktrans(a) = a√(H2 + β) and UV k-2 recovery, plus a horizon-localized bend in the ISW–lensing null-test ratio that probes the relaxation time. We also give a stochastic completion with fluctuation–dissipation relations. A full Einstein–Boltzmann computation in synchronous gauge reveals that for b ≃ 0.07–0.10 the model suppresses the CMB temperature quadrupole by 5–6% while perturbing the acoustic peak amplitudes by less than 1%, naturally reproducing the direction and morphology of the observed Planck low-ℓ power deficit. A joint fit using DESI Data Release 1 BAO, Planck 2018 compressed distance priors, and Pantheon+ supernovae with the full supernova covariance confirms that the preferred background remains close to ΛCDM and does not exclude the b range favored by the low-ℓ analysis. Within the allowed range the model predicts a characteristic scale-dependent suppression of the matter power spectrum localized to k ≲ 10-2 h Mpc-1. The predicted S8 ≡ σ8√(Ωm0/0.3) is expected to remain consistent with the Planck CMB value; we show that the gravitational slip parameter λ is observationally unconstrained by current and planned surveys because its signature is localized to horizon scales. Numerical-analysis scripts and Boltzmann-solver implementation formulas are provided to support reproducibility, with full-likelihood release products deferred to future work.