Final answer:
Gastrulation is the developmental stage where one can first distinguish between protostome and deuterostome embryos due to the onset of their distinct coelom formation processes: schizocoely in protostomes and enterocoely in deuterostomes.
Step-by-step explanation:
One can first distinguish a protostome embryo from a deuterostome embryo during the stage of gastrulation.
This is because it is at this stage that the initial differences in the development of the coelom between protostomes and deuterostomes begin to manifest.
In protostomes, the coelom forms by schizocoely, where cells in the mesoderm split to form the coelom.
On the other hand, in deuterostomes, the coelom forms through enterocoely, as pouches of the endoderm pinch off to become the coelom.
Additionally, the blastopore's developmental fate differs in these two groups, leading to the protostome's mouth and the deuterostome's anus developing at opposite ends.