ABSTRACT Star formation takes place in filamentary molecular clouds which arise by physical processes that take place in the cold neutral medium (CNM). We address the necessary conditions for this diffuse (n ≈ 30 cm−3), cold (T ≈ 60 K), magnetized gas undergoing shock waves, and supersonic turbulence, to produce filamentary structures capable of fragmenting into cluster forming regions. Using ramses and a magnetized CNM environment as our initial conditions, we simulate a 0.5 kpc turbulent box to model a uniform gas with magnetic field strength of 7 μG, varying the 3D velocity dispersion via decaying turbulence. We use a surface density of 320 M⊙ pc−2, representative of the inner 4.0 kpc central molecular zone of the Milky Way and typical luminous galaxies. Filamentary molecular clouds are formed dynamically via shocks within a narrow range of velocity dispersions in the CNM of 5–10 km s−1 with a preferred value at 8 km s−1. Cluster sink particles appear in filaments which exceed their critical line mass, occurring optimally for velocity dispersions of 8 km s−1. Tracking the evolution of magnetic fields, we find that they lead to double the dense star-forming gas than in purely hydro runs. Perpendicular orientations between magnetic field and filaments can increase the accretion rates onto filaments and hence their line masses. Because magnetic fields help support gas, magnetohydrodynamic runs result in average temperatures an order of magnitude higher than unmagnetized counterparts. Finally, we find magnetic fields delay the onset of cluster formation by ∝ 0.4 Myr.