Context: Molecular clouds, which harbor the birthplaces of stars, form out of the atomic phase of the interstellar medium (ISM). To understand this transition process, it is crucial to investigate the spatial and kinematic relationships between atomic and molecular gas. Aims: We aim to characterize the atomic and molecular phase of the ISM and set their physical properties into the context of cloud formation processes. Methods: We study the cold neutral medium (CNM) by means of H$$\tiny{I}$$ self absorption (HISA) toward the giant molecular filament GMF20.0-17.9 (distance=3.5 kpc, length ∼170 pc) and compare our results with molecular gas traced by $$^{13}$$CO emission. We fit baselines of HISA features to H$$\tiny{I}$$ emission spectra using 1st and 2nd order polynomial functions. Results: 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 $$^{13}$$CO is evident towards the eastern part of the filament. The distribution of HISA peak velocities and line widths agrees well with $$^{13}$$CO within the whole filament. The column densities of the CNM probed by HISA are on the order of 1020 cm$$^{−2}$$ while those of molecular hydrogen traced by $$^{13}$$CO are an order of magnitude higher. The column density probability density functions (N-PDFs) of HISA (CNM) and H$$\tiny{I}$$ 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 H$$_2$$N-PDFs show a broad log-normal distribution with a power-law tail suggesting the onset of gravitational contraction. The saturation of H$$\tiny{I}$$ column density is observed at ∼25 M$$_\bigodot$$pc$$^{−2}$$. Conclusions: 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 H2 column density peaks and signs of active star formation.