In this letter, we consider a single-cell downlink non-orthogonal multiple access (NOMA) system using greedy scheduling with quality-based channel-state information (CSI) feedback (QCF), and propose the user selection and power allocation scheme to reduce the physical-layer latency and achieve target data rates while maximizing the sum rate at high signal-to-noise power ratio (SNR). Assuming Rayleigh fading channels, we investigate the transmission time interval index, which quantifies physical-layer latency, the overhead index of CSI feedback, and the average data rate of the proposed scheme. In addition, we show that the sum rates of NOMA and orthogonal multiple access systems using greedy scheduling with QCF are equal at high SNR.