This is my old housemate's current post-doc project. Or rather, this is the current research question of the ERC-funded 'NeoMilk' project. Humans start domesticating cattle and drinking their milk during the 'Linearbandkeramic' period of the Neolithic, or "late stone age", approximately 6,000 BCE. The 'Linearbandkeramic' band is imaginatively so named because of the appearance of distinctive ceramic vessels with linear bands of decoration across Central Europe during this period, and tests on surviving sherds of this pottery display lipid residues which indicate they were used to store or serve cows milk.

As a side note, my housemate's PhD work was on the examination of animal bones to see whether, with the introduction of a new, renewable source of fat and calcium, people were still cracking open the bones of slaughtered animals to eat the bone marrow inside. Turns out they were.

Hi, this question about prehistory would be worth x-posting to our sister sub /r/AskAnthropology. While there are some anthropologists here, there are more there, and with greater focus on earlier time periods.