Quasi-two-dimensional (2D) metal halide perovskites (MHPs) are an emerging material platform for sustainable functional optoelectronics, however the uncontrollable, broad phase distribution remains a critical challenge for applications. This is because the basic principles for controlling multiple phases in quasi-2D MHPs remain poorly understood, due to the rapid crystallization kinetics during the conventional thin-film fabrication process. Herein, a high-throughput automated synthesis-characterization-analysis workflow is implemented to accelerate material exploration in formamidinium (FA)-based quasi-2D MHP compositional space, revealing the early-stage phase growth kinetics which fundamentally determines the phase distributions. We observe that the prominent n=2 2D phase restricts the growth kinetics of 3D-like phases – α-FAPbI3 MHPs where the spacers are coordinated to the surface. δ-FAPbI3 phase further inhibits the growth of 3D-like phases. It is found that thermal annealing is a critical step for proper phase growth, although it can lead to the emergence of unwanted local PbI2 crystallites. Additionally, fundamental insights into the precursor chemistry associated with spacer-solvent interaction that determines the morphologies and microstructures of quasi-2D MHP films are demonstrated. Our high-throughput study provides comprehensive insights into the fundamental principles in quasi-2D MHP phase control and enables new control of the functionalities of complex materials systems for sustainable device applications.