* According to the Big Bang theory, in the early universe at high temperatures when the universe was only a few tens of microseconds old, the phase of matter took the form of a hot phase of quark matter called the quark–gluon plasma (QGP).
* Compact stars (neutron stars). A neutron star is much cooler than 10 K, but gravitational collapse has compressed it to such high densities, that it is reasonable to surmise that quark matter may exist in the core. Compact stars composed mostly or entirely of quark matter are called quark stars or strange stars. 
* QCD matter may exist within the collapsar of a gamma-ray burst, where temperatures as high as 6.7 × 10 K may be generated.
At this time no star with properties expected of these objects has been observed, although some evidence has been provided for quark matter in the cores of large neutron stars.
* Strangelets. These are theoretically postulated (but as yet unobserved) lumps of strange matter comprising nearly equal amounts of up, down and strange quarks. Strangelets are supposed to be present in the galactic flux of high energy particles and should therefore theoretically be detectable in cosmic rays here on Earth, but no strangelet has been detected with certainty.
* Cosmic ray impacts. Cosmic rays comprise a lot of different particles, including highly accelerated atomic nuclei, particularly that of iron. 
Laboratory experiments suggests that the inevitable interaction with heavy noble gas nuclei in the upper atmosphere would lead to quark–gluon plasma formation.
* Quark matter with baryon number over about 300 may be more stable than nuclear matter. This form of baryonic matter could possibly form a continent of stability.