Figural representations of the Buddha first appear about the 2nd c. CE in two separate places, and in each this tradition seems to have developed independently. The first place was Gandhara (Pakistan and Afghanistan borders) in a kingdom influenced by the Hellenistic culture sown by Alexander the Great (who conquered the region centuries earlier). The Gandhara figures clearly show Greek cultural and artistic influence--in the draping of the clothing, in the carving style, and in the features of the images themselves. One can imagine sculptors trained in the Hellenistic aesthetic allowing that to shape their conception and depiction of the Buddha, just as some of the earliest portrayals of Jesus Christ, in the mosaics of Dura Europis, use the conventions associated with Apollo. This is an image of the Future Buddha Maitreya, who was the object of widespread devotion in the early centuries CE (Delhi, National Museum of India).
Here are two more early Gandhara images, again of the bodhisattva (Future Buddha) Maitreya. The Greek-inflenced style is quite clear.
The left-hand image is at The Art Institute of Chicago; the right one (listed as 2nd c. CE) is at The Boston Museum of Fine Arts.
This is a later Gandhara figure dated to the 3rd c. CE. The label for this image identifies the figure as the bodhisattva (Future Buddha) Maitreya, but the image's form has clearly developed to resemble that associated with images of the Buddha himself, including the "extra-cranial protrusion" and the third eye, which were among the physical signs of a spiritually advanced being. Museum of Fine Arts, Boston.
The best-known Gandhara images are identified as bodhisattvas, but the Buddha was also figurally portrayed. This plate-sized tableau depicts the Buddha's parinirvana (that is, the death of his physical body), and the lamentation of the humans and gods surrounding him. The account of his death records his final instructions: for monks to recite the Vinaya (code of conduct) twice a month, for junior monks to respect their seniors and seniors to care for their juniors, and not to mourn his passing (2nd c. CE, Museum of Fine Arts, Boston).
The other major center for early Buddha figures was Mathura, on the Yamuna river in the heart of the north Indian plain. Whereas Gandharan facial features are lean, angular, and sharply-defined, the Mathura figures have round faces, broad cheekbones, and wide, elongated eyes. These differences are so pronounced that these two schools clearly arose independently.
Most Mathura figures were carved from this blotchy red sandstone. The stone was easy to work, but because it was ugly the the images were usually brightly painted. Art Institute of Chicago.
Here's another example of the Mathura style--showing the Buddha's elongated earlobes and the "extra-cranial protrusion." It also shows the splotchy quality associated with that sandstone. This figure is dated ca. 450 CE and was done during the Gupta Dynasty, one of early India's most important dynasties (Museum of Fine Arts, Boston).
After the 2nd century or so figural portrayals of the Buddha seems to have become relatively accepted and common. Even though the earliest construction at Sanchi only portrays the Buddha aniconically, later work shows the Buddha in human form, and thus shows that this had become more or less accepted.