Molecular clouds, which harbor the birthplaces of stars, form out of the atomic phase of the interstellar medium (ISM). We aim to characterize the atomic and molecular phases of the ISM and set their physical properties into the context of cloud formation processes. We studied the cold neutral medium (CNM) by means of $rm HI$ self-absorption (HISA) toward the giant molecular filament GMF20.0-17.9 and compared our results with molecular gas traced by $^{13}rm CO$ emission. We fitted baselines of HISA features to $rm HI$ emission spectra using first and second order polynomial functions. The CNM identified by this method spatially correlates with the morphology of the molecular gas toward the western region. However, no spatial correlation between HISA and $^{13}rm CO$ is evident toward the eastern part of the filament. The distribution of HISA peak velocities and line widths agrees well with $^{13}rm CO$ within the whole filament. The column density probability density functions (N-PDFs) of HISA (CNM) and $rm HI$ emission (tracing both the CNM and the warm neutral medium, WNM) have a log-normal shape for all parts of the filament, indicative of turbulent motions as the main driver for these structures. The $rm H_2$ N-PDFs show a broad log-normal distribution with a power-law tail suggesting the onset of gravitational contraction. The saturation of $rm HI$ column density is observed at $sim$25$rm,M_{odot},pc^{-2}$. We conjecture that different evolutionary stages are evident within the filament. In the eastern region, we witness the onset of molecular cloud formation out of the atomic gas reservoir while the western part is more evolved, as it reveals pronounced $rm H_2$ column density peaks and signs of active star formation.
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