  The origins of matter and radiation in the universe lie in a Hot Big Bang. We
present a number of well-motivated cosmologies in which the Big Bang occurs
through a strong first order phase transition -- either at the end of
inflation, after a period of kination ("Kination-Induced Big Bang"), or after a
second period of vacuum-domination in the early universe ("Supercooled Big
Bang"); we also propose a "Dark Big Bang" where only the dark matter in the
Universe is created in a first-order phase transition much after inflation. In
all of these scenarios, the resulting gravitational radiation can explain the
tentative signals reported by the NANOGrav, Parkes and European Pulsar Timing
Array experiments if the reheating temperature of the Hot Big Bang, and
correspondingly the energy scale of the false vacuum, falls in the range $T_*
\sim \rho_{{\rm vac}}^{1/4} $= MeV--100 GeV. All the same models at higher
reheating temperatures will be of interest to upcoming ground- and space-based
interferometer searches for gravitational waves at larger frequency.
