  The dynamical architecture and compositional diversity of the asteroid belt
strongly constrain planet formation models. Recent Solar System formation
models have shown that the asteroid belt may have been born empty and later
filled with objects from the inner ($<$2~au) and outer regions (>5 au) of the
solar system. In this work, we focus on the implantation of inner solar system
planetesimals into the asteroid belt - envisioned to represent S and/or E- type
asteroids - during the late-stage accretion of the terrestrial planets. It is
widely accepted that the solar system's giant planets formed in a more compact
orbital configuration and evolved to their current dynamical state due to a
planetary dynamical instability. In this work, we explore how the implantation
efficiency of asteroids from the terrestrial region correlates with the timing
of the giant planet instability, which has proven challenging to constrain. We
carried out a suite of numerical simulations of the accretion of terrestrial
planets considering different initial distributions of planetesimals in the
terrestrial region and dynamical instability times. Our simulations show that a
giant planet dynamical instability occurring at $t\gtrapprox5$ Myr -- relative
to the time of the sun's natal disk dispersal -- is broadly consistent with the
current asteroid belt, allowing the total mass carried out by S-complex type
asteroids to be implanted into the belt from the terrestrial region. Finally,
we conclude that an instability that occurs coincident with the gas disk
dispersal is either inconsistent with the empty asteroid belt scenario, or may
require that the gas disk in the inner solar system have dissipated at least a
few Myr earlier than the gas in the outer disk (beyond Jupiter's orbit).
