  Temporal explanations to the Fermi paradox state that the vast scale of the
galaxy diminishes the chances of establishing contact with an extraterrestrial
technological civilization (ETC) within a certain time window. This argument is
tackled in this work in the context of exploration probes, whose propagation
can be faster than that of a colonization wavefront. Extensive computational
simulations have been done to build a numerical model of the dynamics of the
exploration. A probabilistic analysis is subsequently conducted in order to
obtain bounds on the number of ETCs that may be exploring the galaxy without
establishing contact with Earth, depending on factors such as the number of
probes they use, their lifetime and whether they leave some long-term imprint
on explored systems or not. The results indicate that it is unlikely that more
than ~10^2-10^3 ETCs are exploring the galaxy in a given Myr, if their probes
have a lifetime of 50 Myr and contact evidence lasts for 1 Myr. This bound goes
down to ~10 if contact evidence lasts for 100 Myr, and is also shown to be
inversely proportional to the lifetime of probes. These results are interpreted
in light of the Fermi paradox and are compatible with non-stationary
astrobiological models in which a few ETCs have gradually appeared in the
Fermi-Hart timescale.
