Assuming that the exercise does not influence the quality and timing of sleep.
If I do not sleep much the day before, should I train later in the day.
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Delayed Onset Muscle Soreness (DOMS) has nothing to do with time of day unless there is some research I'm unaware of.
Sleep, however, is required for muscle growth and recovery from training, as expressed in the referenced study. You need (roughly, and this changes in certain populations) 7 hours of sleep to fully recover.
...sleep quality was positively associated with muscle strength, and short sleep duration was associated with reduced muscle strength. Even after adjusting for a number of potentially confounding variables, these associations did not change.
So since sleep is required and DOMS has nothing to do with time of day, I'll stick with Ivo's answer that the best time of day to exercise is the time that you'll regularly do it.