<p>This paper examines a new class of linear-quadratic-Gaussian mean-field team problems that encompasses two weakly-coupled cooperative sub-systems (or, sub-populations). Our novel modeling feature is a nested information structure concerning some inter-temporal (drift) evolution, denoted as <i>f</i>: one sub-system can perfectly access or calibrate this <i>f</i>, whereas it becomes completely unknown for another sub-system. Thus, information set regarding <i>f</i> of the latter sub-system is fully inclusive or nested into that of the former sub-system. Additionally, due to the intrinsic <i>team</i> formation, it is impossible for two sub-systems to share or communicate such information of <i>f</i> although they are cooperative towards the same functional. Subsequently, a natural issue is how to realize the optimal performance in term manner, while still retaining necessary decision robustness under this nested information structure. We tackle this issue in the spirit of soft-constraint by introducing a quadratic penalty on the unknown <i>f</i>. The agents in the sub-system with modeling uncertainty treat this unknown disturbance <i>f</i> as an adversarial player, and formulate a worst-case functional through the soft-constraint penalty. Given the nested information of uncertainty, a Stackelberg-type robust analysis can be conducted: the agents in uncertain sub-system will act jointly as (multiple) leaders, while agents without model uncertainty should subsequently act as followers. Moreover, by the principle of person-by-person optimality and stochastic variational analysis, we can construct an auxiliary optimal control problem designed for a representative Stackelberg-type (leader-follower) agent pair. By solving this problem in conjunction with a consistent mean field approximation, we construct a set of decentralized robust team strategies. Subsequent perturbation analysis validates the asymptotic social optimality of these robust Stackelberg strategies.</p>