Studies of stellar populations in early-type galaxies (ETGs) show that the more massive galaxies form earlier and have a shorter star formation history (SFH). In this study, we investigate the initial conditions of ETG formation. The study begins with the collapse of non-rotating post-Big-Bang gas clouds in Milgromian (MOND) gravitation. These produce ETGs with star-forming timescales (SFT) comparable to those observed in the real Universe. Comparing these collapse models with observations, we set constraints on the initial size and density of the post-Big-Bang gas clouds in order to form ETGs. The effective-radius-mass relation of the model galaxies falls short of the observed relation. Possible mechanisms for later radius expansion are discussed. Using hydrodynamic MOND simulations this work thus for the first time shows that the SFTs observed for ETGs may be a natural occurrence in the MOND paradigm. We show that different feedback algorithms change the evolution of the galaxies only to a very minor degree in MOND. The first stars have, however, formed more rapidly in the real Universe than possible just from the here studied gravitational collapse mechanism. Dark-matter-based cosmological structure formation simulations disagree with the observed SFTs at more than 5 sigma confidence.