Antiferromagnetic (AFM) skyrmions are now becoming an intensively studied topic because they can overcome limitations of the skyrmion Hall effect and dipolar field-induced large size of skyrmions. However, most studies of the AFM skyrmions are focusing on the synthetic antiferromagnets consisting of metallic multilayers, but the investigation of AFM topological magnetism in synthetic vdW antiferromagnets is still rare as far as we know. Here, we propose and demonstrate from first-principles calculations and atomic spin model simulations that a variety of AFM topological spin textures, including skyrmion, chiral domain wall, and meron, can be induced in van der Waals (vdW) synthetic antiferromagnets, i.e., $\mathrm{Mn}{\mathrm{Bi}}_{2}\mathrm{Se}{(\mathrm{S})}_{2}{\mathrm{Te}}_{2}$ bilayer and trilayer. We further show that these noncollinear spin textures are closely hinged with stacking properties and possess unique spin dynamics. Our findings provide not only specific material candidates but also a general approach for achieving and controlling AFM topological magnetism in vdW magnets.