  The recently discovered population of interstellar objects presents us with
the opportunity to characterize material from extrasolar planetary and stellar
systems up close. The forthcoming Vera C. Rubin Observatory Legacy Survey of
Space and Time (LSST) will provide an unprecedented increase in sensitivity to
these objects compared to the capabilities of currently operational
observational facilities. We generate a synthetic population of `Oumuamua-like
objects drawn from their galactic kinematics, and identify the distribution of
impact parameters, eccentricities, hyperbolic velocities and sky locations of
objects detectable with the LSST, assuming no cometary activity. This
population is characterized by a clustering of trajectories in the direction of
the solar apex and anti-apex, centered at orbital inclinations of
$\sim90^\circ$. We identify the ecliptic or solar apex as the optimal sky
locations to search for future interstellar objects as a function of survey
limiting magnitude. Moreover, we identify the trajectories of detectable
objects that will be reachable for \textit{in-situ} rendezvous with a dedicated
mission with the capabilities of the forthcoming \textit{Comet Interceptor} or
proposed \textit{Bridge} concept. By scaling our fractional population
statistics with the inferred spatial number density, we estimate that the LSST
will detect of order $\sim 15$ interstellar objects over the course of its
$\sim10$ year observational campaign. Furthermore, we find that there should be
$\sim1-3$ and $\sim0.0007-0.001$ reachable targets for missions with propulsion
capabilities comparable to \textit{Bridge} and \textit{Comet Interceptor},
respectively. These numbers are lower limits, and will be readily updateable
when the number density and size frequency distribution of interstellar objects
are better constrained.
