Energy storage devices are crucial for transitioning to a sustainable energy system, which includes renewable energy sources, electric vehicles, and portable electronics. Solid-state batteries are a promising candidate for next-generation batteries, but they currently struggle with poor cycling performance and high internal resistance. To address these issues, most of the research has focused on reducing contact resistance between the electrolyte and electrodes and using thinner electrolytes. The electrochemical stability window (ESW) is also a crucial property often overlooked. Many papers report an ESW for the Lithium Aluminum Germanium Phosphate (LAGP) solid electrolyte ranging from 3 to 6 V, which is in contrast to theoretical predictions that suggest they should not exceed 1.6 V. This study highlights the significance of enhancing the electrical connection between the electrolyte and current collector in cyclic voltammetry measurements. LAGP glass-ceramic sintered with concurrent crystallization exhibiting ionic conductivity of 4.15 x 10-4 S cm-1 at room temperature was investigated by cyclic voltammetry. The electrical contact was improved by substituting the Au working electrode in the standard Li/LAGP/Au setup, with a composite working electrode made of a mixture of powder solid electrolyte, carbon, and binder, resulting in the Li/ LAGP/LAGP+C/Au modified setup. Our findings reveal an ESW of 3.5 V, which is lower than the values of around 5-6 V reported using conventional setups. The theoretical prediction for ESW is 1.6 V, which discrepancy compared to experimental results can be attributed to the slow kinetics of electrolyte decomposition, which requires an overpotential to be detected.