  We investigate the low transverse momentum heavy quarkonium ($J/\psi$,
$\Upsilon$) productions in the forward rapidity region of $pp$ and $pA$
collisions at the LHC as an important probe to the transverse momentum
tomography of the gluons in hadrons in the Color Glass Condensate (CGC)
framework. By implementing the Sudakov resummation consistently in the CGC
formalism, we achieve an excellent agreement between the improved CGC
calculations and the LHC data. We show that both the small-$x$ and the Sudakov
effects are essential for a complete description of heavy quarkonium
productions in the low transverse momentum region. This provides a solid
foundation to study the small-$x$ gluon saturation in a big nucleus with the
future $pA$ programs at the LHC.
