I have heard somebody mention a sacrifice that was made before the Mahabharata battle began. Please share any information available.
On the first day of the Kurukshetra war, there were countless unnamed warriors who die, before any named characters were killed. The Bhishma Parva describes what was generally going on:
And in that awful combat destructive of heroes, the sire slew the son, the son slew the sire, the sister's son slew the maternal uncle, the maternal uncle slew the sister's son, friend slew friend, and relatives slew kinsmen. Even thus the slaughter took place in that encounter of the Kurus with the Pandavas. And in that frightful and terrible battle in which no consideration was shown (by anybody for anybody).
But the first named character killed in the war was Virata's son Uttara, who was killed by Madri's brother Shalya (who was unfortunately forced to fight on the Kaurava side, as I discuss in this answer):
And Uttara also, the son of Virata, on a tusker with upraised trunk, rushed against the ruler of the Madras. Salya, however, succeeded in checking the unparalleled impetuosity of that prince of elephants rushing quickly towards his car. That prince of elephants, in great wrath, placing his leg upon the yoke of (Salya's) car, killed his four large steeds of excellent speed. The ruler of the Madras then, staying on that car whose steeds had been slain, hurled a dart, all made of iron, and resembling a snake, for slaying Uttara outright. The latter's coat of mail being cut through by that dart, he became totally deprived of his senses and fell down from his elephant's neck, with the hook and the lance loosened from his grasp. And Salya then, taking up his sword and jumping down from his excellent car, and putting forth his prowess, cut off the large trunk of that prince of elephants. His coat of mail pierced all over with a shower of arrows, and his trunk cut off, that elephant uttered a loud shriek and fell down and expired.
The other sons of Virata, the king who hosted the Pandavas during their year in hiding, were also killed in the war, along Virata with himself.