The existence of supermassive black holes (0MBH ≳ 109 M⊙) at a time when the Universe was only about a Gyr old is an open problem in astrophysics and cosmology. The duration for which a supermassive black hole (SMBH) is accreting as a quasar is defined as the quasar lifetime. Proximity zones of quasars probe the highly ionized regions around quasars and have been used to infer their lifetimes. The recent measurements of small proximity zones in a fraction of z ∼ 6 quasars seemed to imply very short lifetimes, making it further challenging to explain the black hole masses at this redshift. In this talk, I will discuss the robustness of some of the assumptions that are usually made to infer quasar lifetimes from proximity zone sizes. I will show that thanks to the short equilibration time of gas inside the proximity zones, small proximity zones can be readily explained by quasars that vary in brightness with a short duty cycle of fduty ∼ 0.1 and short bright periods of ton ∼ 104 yr, even for long lifetimes. I will then show that reconciling this with black hole mass estimates requires the black hole to continue to grow and accrete during its obscured (when it's not visible as a quasar) phase. Further, I will show that incomplete reionization can impede the growth of proximity zones and make them smaller up to 30%, and the quasar host halo mass only affects proximity zones weakly and indirectly.