How young could the asteroid belt be? I heard a theory (possibly from a crackpot) that there was an event in our solar system where two objects collided and created the asteroid belt, the orbits of some of the planets were altered, and that this event took place late enough for homo sapiens to have referenced observations made during the previous orbit in their oral traditions. (Mars parsing close enough to Earth for people to observe its moons)

Is any of this possible given readily observable evidence?
Are asteroid belts ever created in this way?
Dating the age of the asteroid belt is a problem that has to date no general solution. 

Rocks are usually dated in the laboratory via isotopical analysis. This is possible for meteorites, but what to do about those rocks that remain in space?

Several methods to date the asteroid belt are known to me, apart from ad-hoc assumptions that it has the same age as the planets:


Creating links between dated meteorites and asteroid families: The meteorite family of L chondrites have possible origin families in the asteroid belt. Those 'families' are small blobs in the eccentricity-inclination diagrams, that probably originated in one common parent-body breakup event. Dating meteorites originating from those families, gives minimum ages for the parent bodies of i.e. 500 Myrs for the Ordovician meteor event.
Dynamical age modeling: After a breakup of a parent body, the cloud of fragments experience different strengths of YORP and tidal forces, which causes their semimajor axis distribution to spread. Taking a given distribution, one can calculate back to an age of when the cloud was one particle, i.e. the moment of breakup. This again is a minimum age and found for the Flora family to be more than $10^8$, but less than $10^9$ years. This does exclude a very young belt, but does not say much about the upper age limit.
Crater ages: For the largest bodies, i.e. Ceres, Vesta, etc. we can assign relative ages to the lunar cataclysm. Those usually give ages in excess than 3-4 Gyrs. For bodies like Vesta, where the surface is saturated with craters, this age is a lower limit.
Dating of crustal ejecta: There is another family of meteorites that can be linked specifically to Vesta via spectroscopy, called the HED meteorites. Those meteorites look like they're coming from a differentiated parent body (melted, low siderophile element content), and they containt CAIs. Thus, we can date Vesta at least back to the origin of the solar system, as CAIs give us the effective $t0$ for the formation of the solar system.