We study the use of squeezed probe light and evasion of measurement backaction to enhance the sensitivity and measurement bandwidth of an optically pumped magnetometer (OPM) at sensitivity-optimal atom number density. By experimental observation, and in agreement with quantum noise modeling, a spin-exchange-limited OPM probed with off-resonance laser light is shown to have an optimal sensitivity determined by density-dependent quantum noise contributions. Application of squeezed probe light boosts the OPM sensitivity beyond this laser-light optimum, allowing the OPM to achieve sensitivities that it cannot reach with coherent-state probing at any density. The observed quantum sensitivity enhancement at optimal number density is enabled by measurement backaction evasion.