ABSTRACT Observations of high-redshift quasars hosting billion solar mass black holes at z ≳ 6 challenge our understanding of early supermassive black hole (SMBH) growth. In this work, we conduct a near-infrared spectroscopic study of 19 quasars at 6.2 ≲ z ≲ 7.5, using the Folded-port InfraRed Echellette instrument on the 6.5-m Magellan/Baade Telescope. We estimate the single-epoch masses of the quasars’ SMBHs by means of the Mg ii emission line and find black hole masses of $M_{\text{BH}} \approx (0.2\!\!-\!\!4.8)\, \times \, 10^9\ \mathrm{ M}_\odot$. Furthermore, we measure the sizes of the quasars’ proximity zones, which are regions of enhanced transmitted flux bluewards of the Ly $\alpha \,$ emission line, ionized by the quasars’ radiation itself. While it has been shown that the proximity zone sizes correlate with the quasars’ lifetimes due to the finite response time of the intergalactic medium to the quasars’ radiation, we do not find any correlation between the proximity zone sizes and the black hole mass, which suggests that quasar activity and the concomitant black hole growth are intermittent and episodic.