  We consider the evolution of traversable wormhole geometries in the
inflationary, radiation -- and matter -- dominated eras, and dynamic wormholes
with a traceless energy-momentum tensor (EMT), within the recently proposed
{\it pole dark energy} model. We show that the evolving radiation -- and matter
-- dominated wormhole spacetimes satisfy the null energy condition (NEC), but
possess negative energy densities at late times, thus violating the weak energy
condition (WEC) in this specific domain. However, we demonstrate with a
specific example that the traceless EMT evolving wormholes, supported by
conformally invariant massless fields, in principle, could satisfy the WEC, and
consequently the NEC, at all times and for all values of the radial coordinate.
Thus, one may imagine a scenario in which these geometries originate in the
Planckian era through quantum gravitational processes. Inflation could then
provide a natural mechanism for the enlargement of these Planckian wormholes,
where their FLRW background evolution is governed by pole dark energy. For the
first time in the literature, specific dynamical $4$-dimensional solutions are
presented that satisfy the NEC and WEC everywhere and everywhen.
