Gauss constructed these units by considering the value of the permittivity of free space

$$ \epsilon_0 = \frac{1}{4\pi} $$

which makes Coulomb‘s law very simple by making $4\pi\epsilon_0=1$ giving rise to the electric field

$$ E = \frac{q}{r^2} $$

that is a charge $q$ creates an electric field of magnitude $E$ at a distance $r$.