The steady laminar flow past a time-dependent radially stretching sheet within a hybrid nanofluid is studied. The governing equations are converted into ordinary differential equations utilizing the similarity transformations. Successive linearization is applied to linearize the nonlinear system of equations. The resultant system of equations is solved using the Chebyshev collocation method. Plots demonstrating velocity, temperature, Nusselt number, and skin friction coefficient for a few chosen parameters are shown. When volume fractions of Cu-containing nanoparticles rise, the critical values of these parameters fall, and when alumina (Al2O3) nanoparticle volume fractions rise, they increase. Compared with the nanofluid on the radially stretched surface, the hybrid nanofluid transfers heat faster. The addition of more alumina nanoparticles also lowers the Nusselt number and raises the skin friction coefficient. Furthermore, adding more copper (Cu) nanoparticles lowers the skin friction coefficient and the local Nusselt number on the stretching surface. This study is important because it demonstrates how hybrid nanofluids can be engineered to optimize heat transfer and flow resistance over stretching surfaces, providing valuable guidance for improving thermal performance in industrial and engineering applications.