The Atlantic Meridional Overturning Circulation (AMOC) is a critical tipping element in the Earth system. While parametric uncertainty in climate models represents a dominant source of uncertainty in future projections, particularly regarding non-linear tipping phenomena, it has been largely ignored or overlooked in previous studies based on the CMIP6 model ensemble which have predominantly focused on structural uncertainties. To address this fundamental gap, this study investigates AMOC predictability by performing an uncertainty quantification (UQ) that explicitly accounts for parametric uncertainty. Crucially, this work represents the first application of an Observing System Simulation Experiment (OSSE) framework to an Earth System Model (ESM)-based AMOC predictability study under parametric uncertainty. Utilizing the Earth system model of intermediate complexity, LOVECLIM, we conduct an OSSE by varying 25 key uncertain parameters under a freshwater hosing scenario. To mitigate the prohibitive computational cost of coupled model simulations, we construct a high-fidelity surrogate model combining Principal Component Analysis (PCA) and Gaussian Process Regression (GPR) and realize efficient Surrogate-model Uncertainty Quantification, which effectively utilizes Perturbed Parameter Ensembles (PPEs). Our pseudo-observation experiments demonstrate that assimilating contemporary Sea Surface Salinity (SSS) data effectively constrains critical parameters governing freshwater transport, showing the best efficacy in reducing future AMOC projection uncertainty. Even though Sea Surface Temperature (SST) or other atmospheric observations reduce parametric and simulation accuracy in the observation period, the current AMOC and future AMOC prediction uncertainty is not reduced very well.