Although there's evidence for chemiosmotic methanogens using methane-originating electrons to boil water to turn an ATP synthase turbine as far back as the know

Although there's evidence for chemiosmotic methanogens using methane-originating electrons to boil water to turn an ATP synthase turbine as far back as the known Hadean rock inclusions in the Pilbara craton, the article specifies "complex life", not however defining it. They leave that to the paper, which uses a fairly common standard for defining complex life: the development of segregated and access-controlled cell nuclei. There is literature from as far back as 2011 suggesting that the spindles necessary for nuclei to work cannot be maintained by an organism that can only get 2 ADP->ATP reactions per molecule of glucose burned and instead need a floor of about 11 to 14, but the method bacteria use to get 38 ATP per glucose does depend on photosynthesis.