This study presents a new class of poly-Genocchi polynomials constructed through the integration of some interesting polynomials. The resulting family, referred to as the multivariable generalized Hermite-type-Genocchi polynomials of order a, is investigated in detail. Several fundamental properties are derived, including explicit representations, addition formulas, and polynomial expansions. In addition, relationships between this new family of polynomials and a certain generalized Stirling numbers of the first kind are established.