In response to pressing energy crises and environmental concerns, enhancing the performance of existing energy conversion systems, such as gas turbines, and tapping into renewable resources have become critical imperatives. Escalating ambient temperatures poses a notable challenge, hampering the efficiency of gas turbines. This study rigorously explores the feasibility of earth-to-air heat exchangers (EAHEs) as a pragmatic solution to cool gas turbine inlet air. The primary objective is an exhaustive techno-economic analysis evaluating the long-term operational viability of EAHE systems. Employing the Taguchi method, the study optimizes the system geometry and pipe arrangement, focusing on four key control factors: pipe diameter, spacing, length, and depth. The pivotal optimization criterion is the levelized cost of energy (LCOE), encompassing thermal performance and economic viability. The net present value (NPV) and Discounted Payback Period provide supplementary insights into the economic prospects. Integral to the study is a novel and intricate hybrid analytical-numerical model that simulates the long-term transient operation of EAHE. Findings from a detailed case study unveil an optimized scenario yielding an LCOE amounting to 0.071 $/kWh, accompanied by a substantial NPV of 4.5 million dollars.