Context. The large-scale linear halo bias encodes the relation between the clustering of dark-matter (DM) halos and that of the underlying matter density field. Although the primary dependence of bias on halo mass is well understood in the context of structure formation, the physical origins of the multiple additional relations at fixed halo mass, commonly known as secondary halo bias, have not been fully elucidated. Of particular relevance is the secondary dependence on the halo assembly history, known as halo assembly bias. Aims. Our goal is to determine whether the properties of the initial regions from which z = 0 halos originate produce any secondary bias at z = 0. By analyzing these initial dependences in connection with halo assembly bias, we intend to provide insight into the physical origins of the effect. Methods. We selected halos at z = 0 in the IllustrisTNG DM-only simulation and traced back the positions and velocities of their DM particles to z = 12. The resulting initial regions were characterized according to several shape-related and kinematic properties. The secondary bias signal produced by these properties at z = 0 was measured using an object-by-object bias estimator, which offers significant analytical advantages as compared to the traditional approach. Results. We show that, when split by the properties of their initial DM clouds, z = 0 halos display significant secondary bias, clearly exceeding the amplitude of the well-known halo assembly bias signal produced by concentration and age. The maximum bias segregation is measured for cloud velocity dispersion and radial velocity, followed by cloud concentration, sphericity, ellipticity, and triaxiality. We further show that both velocity dispersion and radial velocity are also the properties of the initial clouds that most strongly correlate with halo age and concentration at fixed halo mass. Our results highlight the importance of linear effects in shaping halo assembly bias.