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If you shot a round of stars with inaccurate time, you still get your latitude.   There is no way to get acccurate time back without seeing the moon, taking a sight from a known position or seeing an eclipse of one on Jupiter's moons.

If you can see the moon you can do a lunar or use the Letcher method to cross a moon line with a round of stars.

If you are at a known position you can shot a body, plot the line relative to where you know you are then adjust the time and replot until you get the line thru the known position, then the time is correct.

If you have a reasonable telescope you can watch the moons of Jupiter for eclipses and reappearances.  With an appropriate ephemeris you can get time.  This was a very old method of checking universal time.  Of course Jupiter has to be in the night half of the sky for this to work.