If a space-faring civilization embarks on a program to send probes to interstellar destinations, the first probe to arrive at such a destination is not likely to be one of the earliest probes, but one of much more advanced capability. This conclusion is based on a scenario in which an extraterrestrial civilization (ETC) embarks upon an interstellar program during which it launches increasingly sophisticated probes whose departure speed increases as a function of time throughout the program. Two back-of-the-envelope models are considered: one in which the launch velocity of an outgoing vehicle increases linearly with the time of launch, and a second in which the increase is exponential with launch date. In this paper consideration is directed to an hypothesized probe arriving within the Solar System from a non-terrestrial civilization. Within the above scenarios, a first-encounter probe will be one that was launched well after the initiation of an interstellar program by an ETC. Consequently, such a probe would be the product of a relatively advanced phase of that ETC's technology. The more distant the site from which an ETC is launching probes, the greater will be the technology gap between a first-encounter probe and terrestrial technology. One possible ramification may pertain to interpreting the nature of Unidentified Aerial Phenomena (UAP). Are flight characteristics of any UAP singular enough as to be consistent with an origin from a distant ETC?