Proteins are biosynthesized from N to C terminus before they depart from the ribosome and reach their bioactive state in the cell. At present, very little is known about the evolution of conformation and the free energy of the nascent protein with chain elongation. These parameters critically affect the extent of folding during ribosome-assisted biosynthesis. Here, we address the impact of vectorial amino acid addition on the burial of nonpolar surface area and on the free energy of native-like structure formation in the absence of the ribosomal machinery. We focus on computational predictions on proteins bearing the globin fold, which is known to encompass the 3/3, 2/2, and archaeal subclasses. We find that the burial of nonpolar surface increases progressively with chain elongation, leading to native-like conformations upon addition of the last C-terminal residues, corresponding to incorporation of the last two helices. Additionally, the predicted folding entropy for generating native-like structures becomes less unfavorable at nearly complete chain lengths, suggesting a link between the late burial of nonpolar surface and water release. Finally, the predicted folding free energy takes a progressive favorable dip toward more negative values, as the chain gets longer. These results suggest that thermodynamic stabilization of the native structure of newly synthesized globins during translation in the cell is significantly enhanced as the chain elongates. This is especially true upon departure of the last C-terminal residues from the ribosomal tunnel, which hosts ca., 30-40 amino acids. Hence, we propose that release from the ribosome is a crucial step in the life of single-domain proteins in the cell.