My very first hat was the demo's stovepipe, about a month after the hats originally came out. A little later, I found something else (I believe it was the camera beard) and crafted them both together and received the heavy's football helmet, which I still wear to this day.
My first hat was an Engineer Mining Light, I got it 2 hours after hats came out in the update. The next day, I got another Mining Light. Haven't gotten a hat dropped yet... and I have over 1200 game hours logged since then.