Using the framework of wedge dynamics, we compute the effective transverse mass of a soft quark mode propagating in the expanding background of hard quarks and gluons created at the earliest time of the collision. We discover that the wedge dynamics does not require any external infrared or collinear cutoff. The effective mass is produced mainly due to the forward quark-quark scattering mediated by the longitudinal (in the sense of Gauss law) magnetic fields. Contribution of the radiation field is parametrically suppressed.