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We solve for the gluon generalized parton distributions (GPDs) inside the proton at zero skewness, focusing specifically on leading twist chiral-even GPDs. We obtain and employ the light-front wavefunctions (LFWFs) of the proton from a light-front quantized Hamiltonian with Quantum Chromodynamics input using basis light-front quantization (BLFQ). Our investigation incorporates the valence Fock sector with three constituent quarks and an additional Fock sector, encompassing three quarks and a dynamical gluon. We examine the GPDs within impact parameter space and evaluate the x-dependence of the transverse square radius. We find that the transverse size of the gluon at lower-x is larger than that of the quark, while it exhibits opposite behavior at large-x. Using the proton spin sum rule, we also determine the relative contributions of quarks and the gluon to the total angular momentum of the proton.