It is certainly feasible. If you are on Earth within about 10,000 years of the present, you should be able to figure out the date, time and your position after about 24 hours of observations. However, if you are further in the past or future, the constellations will start to look different and a lot more observation may be needed.
Locating Polaris gives you the north direction and your latitude. Time-laps photography can confirm the direction of Earth’s axis (it wobbles in 26000 year cycle). Position of planets and the Moon would give you date to within a few days. However, you may not see enough of them, giving you even dozens of possibilities. But seeing the direction where the Sun rises should rule out most of them. Once you are sure of the date, position of planets and the Moon will allow you to find your longitude. The Sun at its highest position will set the local noon, and knowing your position, calculating the UTC is dead simple.
The same applies to other places in the Solar system, the stars do not really change much and planets are of course the same. However, the movement of the body you are standing on is probably known will less precision than the Earth, so you may need to observe the sky for a couple of days.
Outside of the Solar system you are out of luck. If you can find the center of Milky Way (very difficult with visual observations) and compare it to objects outside of our galaxy (say Andromeda), you should be able to get a rough idea where you are in the galaxy - keeping in mind that the Galaxy rotates every 50 million years. Beyond that, trying to identify known stars would very very difficult.