Well, you may want to re-state your question. There are numerous multi-cellular organisms without a nervous system. So you could say that they never sleep: sponges, plants, mushrooms.
This paper on the evolution of sleep concludes:
A phylogenetic evaluation of sleep demonstrates that all
mammals, birds, and reptiles engage in sleep, and evidence
for sleep in amphibians, ﬁshes, and invertebrates is strong if
So it seems that once you have a nervous system, you also have some rest periods. However, it may not be clear if the rest periods are dictated by the lifestyle (e.g. nocturnal foraging) or by a requirement to "recharge" the nervous system.