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. We explain the excitation of PSSWs by exchange coupling between forced magnetization precessions in the YIG and CoFeB layers. If the amplitudes of these precessions are different, a dynamic exchange torque is generated, causing the emission of spin waves from the interface. PSSWs form when the wave vector of the spin waves matches a perpendicular confinement condition. PSSWs are not excited if exchange coupling between YIG and CoFeB is eliminated by a 10 nm Ta spacer layer. Micromagnetic simulations confirm the exchange-torque-driven mechanism.