My guess is that incipient capitalism became possible with the Neolithic agricultural revolution 10,000 years ago, which led to settlements and eventually towns and cities. Settled farmers would occasionally produce surpluses. Those surpluses were the first capital. Capitalism can’t exist at the purely subsistence level; if that level has any economy at all, it is a barter economy.
Capitalism requires capital (surplus), some medium of exchange, merchants, and fixed settlements to get started. No doubt this took a long time and was mostly hit or miss. When those merchants began to travel to nearby settlements, they took the first steps toward the global capitalism that envelopes us now.
Until I get a WayBack Machine, that’s my best guess. :)
You make a good point about the hostility between capitalism and free enterprise. Monopoly is capitalism’s poison pill. All modern, late stage capitalists loathe competition. The want to be and own the market. Free enterprise is anathema to them. Why this is so hard for people to see, I don’t know.