  The $X(6900)$ resonance, originally discovered by the \texttt{LHCb}
collaboration and later confirmed by both \texttt{ATLAS} and \texttt{CMS}
experiments, has sparked broad interests in the fully-charmed tetraquark
states. Relative to the mass spectra and decay properties of fully-heavy
tetraquarks, our knowledge on their production mechanism is still rather
limited. In this work we investigate the inclusive production of fully-charmed
$S$-wave tetraquarks at \texttt{LHC} within the nonrelativistic QCD (NRQCD)
factorization framework. The partonic cross sections are computed at lowest
order in $\alpha_s$ and velocity, while the long-distance NRQCD matrix elements
are estimated from phenomenological potential models. We predict the
differential $p_T$ spectra of various fully-charmed $S$-wave tetraquarks at the
\texttt{LHC}, and compare with the results predicted from the fragmentation
mechanism at large $p_T$ end.
