Spin waves in ferrimagnetic yttrium iron garnet (YIG) films with ultralow magnetic damping are relevant for magnon-based spintronics and low-power wave-like computing. The excitation frequency of spin waves in YIG is rather low in weak external magnetic fields because of its small saturation magnetization, which limits the potential of YIG films for high-frequency applications. Here, we demonstrate how exchange-coupling to a CoFeB film enables efficient excitation of high-frequency perpendicular standing spin waves (PSSWs) in nanometer-thick (80 nm and 295 nm) YIG films using uniform microwave magnetic fields. In the 295-nm-thick YIG film, we measure intense PSSW modes up to 10th order. Strong hybridization between the PSSW modes and the ferromagnetic resonance mode of CoFeB leads to characteristic anti-crossing behavior in broadband spin-wave spectra. A dynamic exchange torque at the YIG/CoFeB interface explains the excitation of PSSWs. The localized torque originates from exchange coupling between two dissimilar magnetization precessions in the YIG and CoFeB layers. As a consequence, spin waves are emitted from the YIG/CoFeB interface and PSSWs form when their wave vector matches the perpendicular confinement condition. PSSWs are not excited when the exchange coupling between YIG and CoFeB is suppressed by a Ta spacer layer. Micromagnetic simulations confirm the exchange-torque mechanism.