  A numerical semigroup is said to be universally free if it is free for any
possible arrangement of its minimal generating set. In this work, we establish
that toric ideals associated with universally free numerical semigroups can be
generated by their set of circuits. Additionally, we provide a characterization
of universally free numerical semigroups in terms of Gr\"obner bases.
Specifically, a numerical semigroup is universally free if and only if all
initial ideals of its corresponding toric ideal are complete intersections.
Furthermore, we establish several equalities among the toric bases of a
universally free numerical semigroup.
  We provide a complete characterization of $3$-generated universally free
numerical semigroups in terms of their minimal generating sets, and by proving
the equality of certain toric bases. We compute exactly all the toric bases of
a toric ideal defined by a 3-generated universally free numerical semigroup.
Notably, we answer some questions posed by Tatakis and Thoma by demonstrating
that toric ideals defined by $3$-generated universally free numerical
semigroups have a set of circuits and a universal Gr\"obner basis of size 3,
while the universal Markov basis and the Graver basis can be arbitrarily large.
We present partial results and propose several conjectures regarding
universally free numerical semigroups with more than three generators.
