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.