This work aims to examine the (non)linear properties of the dust-acoustic waves (DAWs) in a polarized superthermal complex magnetoplasma. The existing plasma model consists of inertial dust grains and inertialess electrons and ions. The electrons in this model adhere to the Maxwell–Boltzmann distribution, while the ions conform to the superthermal distribution. It is postulated that the electrostatic waves propagate obliquely with the magnetic field. The Sagdeev potential approach is employed to reduce the basic model equations to an equivalent energy balance equation. It is shown how the existence domain and the properties of large amplitude obliquely propagating dust-acoustic solitary waves (DASWs) are affected via the characteristic relevant plasma parameters. The implication of the study is highlighted to the space dusty plasma.