We shed light on the interplay between structure and many-body effects relevant for itinerant ferromagnetism in LaAlO3/SrTiO3 heterostructures. The realistic correlated electronic structure is studied by means of the (spin-polarized) charge self-consistent combination of density-functional theory with dynamical mean-field theory beyond the realm of static correlation effects. Though many-body behavior is also active in the defect-free interface, a ferromagnetic instability occurs only with oxygen vacancies. A minimal Ti two-orbital e(g) -t(2g) description for the correlated subspace is derived. Magnetic order affected by quantum fluctuations builds up from effective double exchange between modified nearly localized e(g) and mobile xy electrons.