You're making a lot of assumptions here and basing it on the limited knowledge of a specifies that has failed to make any significant strides into exploring anything other than its own solar system.
There's an easy answer that coincides with our current understanding of physics. Then there is "Aliens have discovered tech that makes it easier for them to fling a half mile long object vs a satellite sized object across the stars at a relatively slow speed."
Sorry if I take "explosion makes rock go far" as being the more plausible explanation than "Aliens want to wait a million years for a brief glimpse at a distant solar system".
It's not the size/volume that matters, but the mass. Even with our limited science and technology, we have designs for interplanetary ships that drag hundreds of meters of radiator surface with them. It's not hard to imagine - and it has been imagined many times - a ship that consists of a core with a gigawatt-range powerplant, reaction mass, efficient engines, and kilometer-long radiators to dump the powerplant heat into space. If anything, based on our knowledge and assuming no magitech breakthroughs in space propulsion, you should expect interstellar ships to be large but light, maximizing surface area while minimizing mass.
To be fair, there is no need for the probe to have been designed for a mission to our star system. It could be that it was a craft meant for something else entirely that left its star system, like our Voyager probes have, and drifted for eons before happening to pass through our star system and be observed.
Of course, that is still less likely than some unusual rock doing the same thing.
Sure, just a bunch of energy for such a large object. "To see if they can" may very well be a reason, but that doesn't seem likely for a species that advances far enough to be able to accomplish such an achievement.
> Sorry if I take "explosion makes rock go far" as being the more plausible explanation than "Aliens want to wait a million years for a brief glimpse at a distant solar system".
Playing Devil's advocate, a probe that size would likely visit many star systems, the Solar being a random one in the bunch. The brief pass would be necessary to avoid the energy expenditure of braking and reaccelerating.
Sorry if I take "explosion makes rock go far" as being the more plausible explanation than "Aliens want to wait a million years for a brief glimpse at a distant solar system".