Context. The vast majority of the geophysical and geological constraints (e.g., internal structure, cratering history) for main-belt asteroids have so far been obtained via dedicated interplanetary missions (e.g., ESA Rosetta, NASA Dawn). The high angular resolution of SPHERE/ZIMPOL, the new-generation visible adaptive-optics camera at ESO VLT, implies that these science objectives can now be investigated from the ground for a large fraction of D ≥ 100 km main-belt asteroids. The sharp images acquired by this instrument can be used to accurately constrain the shape and thus volume of these bodies (hence density when combined with mass estimates) and to characterize the distribution and topography of D ≥ 30 km craters across their surfaces. Aims. Here, via several complementary approaches, we evaluated the recently proposed hypothesis that the S-type asteroid (89) Julia is the parent body of a small compact asteroid family that formed via a cratering collisional event. Methods. We observed (89) Julia with VLT/SPHERE/ZIMPOL throughout its rotation, derived its 3D shape, and performed a reconnaissance and characterization of the largest craters. We also performed numerical simulations to first confirm the existence of the Julia family and to determine its age and the size of the impact crater at its origin. Finally, we utilized the images/3D shape in an attempt to identify the origin location of the small collisional family. Results. On the one hand, our VLT/SPHERE observations reveal the presence of a large crater (D ~ 75 km) in Julia’s southern hemisphere. On the other hand, our numerical simulations suggest that (89) Julia was impacted 30–120 Myrs ago by a D ~ 8 km asteroid, thereby creating a D ≥ 60 km impact crater at the surface of Julia. Given the small size of the impactor, the obliquity of Julia and the particular orientation of the family in the (a,i) space, the imaged impact crater is likely to be the origin of the family. Conclusions. New doors into ground-based asteroid exploration, namely, geophysics and geology, are being opened thanks to the unique capabilities of VLT/SPHERE. Also, the present work may represent the beginning of a new era of asteroid-family studies. In the fields of geophysics, geology, and asteroid family studies, the future will only get brighter with the forthcoming arrival of 30–40 m class telescopes like ELT, TMT, and GMT.