Nothing can substitute for sleep because sleep is not just resting. It's a physical state in which life-critical biological housekeeping gets done. The human body can't clean and repair its brain while the brain is in operating in conscious mode. If you want to make your humans do without sleep, then you just need to make up a reason, like they meditate and reconnect with the spirits of the ancestors, who then magically rejuvenate them or something. Or, you can just say they meditate, and your reader will probably forgive you if the story is a good read.
Humans can't retain the benefits of sleep through meditation, because a critical function of sleep is to remove metabolic toxins from the brain. Meditation doesn't do that. The buildup of the metabolic toxins causes some of the effects of sleep deprivation and if enough toxins accumulate, they cause neuron damage and cell death.
"The brain only has limited energy at its disposal and it appears that it must choose between two different functional states — awake and aware or asleep and cleaning up. You can think of it like having a house party. You can either entertain the guests or clean up the house, but you can't really do both at the same time."
The brain also assists the body with healing during sleep by releasing hormones that promote healing, among other things. Lack of sleep has a host of bad health effects which would probably lead to an early death.
"The physical healing of wounds is expedited by sleep, and sleep strengthens the immune system in general. Rats deprived of sleep in experiments show distinctly inferior healing capacities, develop skin lesions, lose body mass, and are unable to maintain a stable body temperature, ultimately dying of sepsis or just “exhaustion”. Sleep-deprived rats have been shown to exhibit substantially fewer leukocytes (white blood cells), the body’s main defence against infection, and sleep-deprived humans show less than half of the protective antibodies after an inoculation jab as compared to people with healthy sleep patterns."
If you want to know more, just do an internet search for the terms sleep brain metabolic clean and sleep allow body heal.