  Using the small-$x$ Improved Transverse Momentum Dependent factorization
(ITMD), which, for a general two-to-two massless scattering can be proved
within the Color Glass Condensate (CGC) theory for transverse momenta of
particles greater than the saturation scale, we provide predictions for
isolated forward photon and jet production in proton-proton and proton-nucleus
collisions within the planned ALICE FoCal detector acceptance. We study
azimuthal correlations, $p_T$ spectra, as well as normalized ratios of
proton-proton cross sections for different energies. The only TMD distribution
needed for that process is the "dipole" TMD gluon distribution, which in our
computations is based on HERA data and undergoes momentum space BK evolution
equation with DGLAP corrections and Sudakov resummation. We conclude, that the
process provides an excellent probe of the dipole TMD gluon distribution in
saturation regime.
