The most distant quasars known, at redshifts z approximately 6, generally have properties indistinguishable from those of lower-redshift quasars in the rest-frame ultraviolet/optical and X-ray bands. This puzzling result suggests that these distant quasars are evolved objects even though the Universe was only seven per cent of its current age at these redshifts. Recently one z approximately 6 quasar was shown not to have any detectable emission from hot dust, but it was unclear whether that indicated different hot-dust properties at high redshift or if it is simply an outlier. Here we report the discovery of a second quasar without hot-dust emission in a sample of 21 z approximately 6 quasars. Such apparently hot-dust-free quasars have no counterparts at low redshift. Moreover, we demonstrate that the hot-dust abundance in the 21 quasars builds up in tandem with the growth of the central black hole, whereas at low redshift it is almost independent of the black hole mass. Thus z approximately 6 quasars are indeed at an early evolutionary stage, with rapid mass accretion and dust formation. The two hot-dust-free quasars are likely to be first-generation quasars born in dust-free environments and are too young to have formed a detectable amount of hot dust around them.