It’s been shown in so many studies as to be beyond question:
Read those studies. And there are many more. The effect of sleep or lack thereof is so dramatic that we find people with mismanaged stress can DO EVERYTHING ELSE RIGHT and simply lose muscle and gain fat when they think they “should” lose fat and even maintain muscle. Stress is real. Again, this is why simple calories explanations abjectly fail at helping most people achieve health and fitness.
Don’t underestimate stress management. You can diet and exercise at a freakish level and make ZERO progress if overall life balance is rocky and stress is overwhelming.
So, how about that sleep component? How can we optimize? There are the obvious hacks, like regularizing sleep and wake times, getting away from screens, and so on. But you might not know that gut microbes play a substantive role.
Recent research has uncovered that your gut microbes influence your sleep: http://www.tsukuba.ac.jp/en/research-list/p202011271448. So, in part, our symbionts come up in the explanatory model for another facet of health.
It makes sense on multiple fronts, because overstressed people have damaged gut flora. The causal pathway is bidirectional: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6290721/. That is, suboptimal gut health means poor stress management. Poor stress management means reduction in diversity and count of beneficial bacteria. Sleep cycles manage microbes and microbes manage circadian cascades.
Microbiome diversity is positively correlated with effective and efficient sleep: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6779243/.
So, as odd as it may seem to you, starting with caring for your anaerobic bacteria is one of the most profound paths to good sleep. Good sleep is the strongest salvo you can make on fat loss. To change body comp, begin with restoring the gut and improving resilience against stress.