**Core Concept**
The formation of the prochordal plate and the primitive streak is a crucial event in embryonic development, marking the initiation of gastrulation. This process involves the coordinated movement of cells, which eventually gives rise to the three primary germ layers: ectoderm, mesoderm, and endoderm. The prochordal plate is a critical structure that will eventually develop into the oral ectoderm and the anterior portion of the notochord.

**Why the Correct Answer is Right**
The correct answer is related to the timing of gastrulation, which typically occurs around 2-3 weeks post-fertilization in humans. During this period, the prochordal plate and the primitive streak form, and the embryo undergoes a series of cellular movements, including epiboly, involution, and delamination. The primitive streak is a linear structure that will eventually give rise to the mesoderm and the notochord. The prochordal plate, on the other hand, will contribute to the formation of the oral ectoderm and the anterior portion of the notochord.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not accurately reflect the timing of gastrulation. Gastrulation typically occurs around 2-3 weeks post-fertilization, not at the time of implantation.

**Option B:** This option is incorrect because it is not specific enough. While it is true that the prochordal plate and the primitive streak form during gastrulation, it does not provide a precise answer.

**Option D:** This option is incorrect because it is too late. The prochordal plate and the primitive streak form during the early stages of gastrulation, not during organogenesis.

**Clinical Pearl / High-Yield Fact**
The formation of the prochordal plate and the primitive streak is a critical event in embryonic development, and abnormalities in this process can lead to various congenital anomalies, including neural tube defects and gastrointestinal anomalies. Understanding the timing and mechanisms of gastrulation is essential for comprehending the development of the human embryo.

**Correct Answer:** C.