In this study, we explore specific categories of f (G, T) gravity, which hold promise in terms of their ability to explain phenomena such as dark energy and the inflationary epoch. Our aim is to examine the general formalism and illustrate how various evolutions related to inflation and dark energy can be accounted for within the framework of f (G, T) gravity. We propose a unified model where f (G, T) gravity governs both early and late-time dynamics, leading to inflation and the dark energy phase, while resembling ordinary Einstein-Hilbert gravity during an intermediate era. The specific expression we consider for the f (G, T) theory is f (G, T) = G + mG 2 + nT , where m and n are free parameters. To solve the field equation, we utilize a specialized formulation of the deceleration parameter, represented as q = α + βH, where α and β being model parameters. We then determine the optimal values for these model parameters by fitting them to the latest observational datasets, including 57 data points from the Cosmic Chronometers datasets, Pantheon datasets, and BAO datasets.Furthermore, we analyze the physical behavior of cosmographic parameters corresponding to the constrained values of the model parameters, as well as the energy density and pressure. The evolution of the deceleration parameter predicts a transition from a decelerated phase to an accelerated phase of the Universe. Remarkably, our f (G, T) cosmological model effectively describes the observed cosmic acceleration in the late-time universe, thereby eliminating the need to introduce a dark energy component in the field equations.