  We show that a simple sub-class of Horndeski theory can describe a time
crystal Universe. The time crystal Universe can be regarded as a baby Universe
nucleated from a flat space, which is mediated by an extension of
Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory.
Remarkably, when a cosmological constant is included, de Sitter Universe can be
created by tunneling from the time crystal Universe. It gives rise to a past
completion of an inflationary Universe.
