TSH is released in a series of pulses, usually beginning around when your body thinks is bedtime. Most people have a peak in TSH between 9pm and 2am, and it falls steadily throughout the day until the next series of pulses. If there was such a thing as all-night labs, maybe more hypothyroid people could get diagnosed.
The next best option would be first thing when their doors open in the a.m.
Food will have no effect on thyroid labs.