Neutron diffraction on the centrosymmetric square-net magnet EuGa2Al2 reveals multiple incommensurate magnetic states (AFM1, 2, 3) in zero field. In applied field, a new magnetic phase (A) is identified from magnetization and transport measurements, bounded by two of the μ0H=0 incommensurate magnetic phases (AFM1, helical, and AFM3, cycloidal) with different moment orientations. Moreover, magnetotransport measurements indicate the presence of a topological Hall effect, with maximum values centered in the A phase. Together, these results render EuGa2Al2 a material with noncoplanar or topological spin texture in applied field. X-ray diffraction reveals an out-of-plane (OOP) charge density wave (CDW) below TCDW∼50 K while the magnetic propagation vector lies in plane below TN=19.5 K. Together these data point to a new route to realizing in-plane noncollinear spin textures through an OOP CDW. In turn, these noncollinear spin textures may be unstable against the formation of topological spin textures in an applied field.