placement of ellipsoids in a cube


I am not yet a lammps user, but I am wondering,
if it is the right tool for solving the following problem:

Given a set of ellipsoids with varying radii and fixed
orientations, I want to place them "randomly" inside
a cube without that they intersect. The number of
ellipsoids may be high, and the density varies.
With randomly I mean that they don't all are at the
bottom of the cube due to gravity, or that there
is a size gradient.

Can that be easily solved, and are there example

Best regards,