Quantum computing holds the potential for quantum advantage in optimization problems, which requires advances in quantum algorithms and hardware specifications. Adiabatic quantum optimization is conceptually a valid solution that suffers from limited hardware coherence times. In this sense, counterdiabatic quantum protocols provide a shortcut to this process, steering the system along its ground state with fast-changing Hamiltonian. In this work, we take full advantage of a digitized-counterdiabatic quantum optimization algorithm to find an optimal solution of the p-spin model up to four-local interactions. We choose a suitable scheduling function and initial Hamiltonian such that a single-layer quantum circuit suffices to produce a good ground-state overlap. By further optimizing parameters using variational methods, we solve with unit accuracy two-spin, three-spin, and four-spin problems for 100%, 93%, and 83% of instances, respectively. As a particular case of the latter, we also solve factorization problems involving 5, 9, and 12 qubits. Due to the low computational overhead, our compact approach may become a valuable tool towards quantum advantage in the NISQ era.