I'm not sure what your composter looks like. I'm used to either a barrel composter where you rotate it by turning a handle or something that sits on the ground. You say yours has a bottom. I don't know how much that changes things in how to operate it. Since it's not sitting in dirt it's probably a good idea to toss a shovelful of dirt in there to introduce microbes. They will eventually show up anyway but any topsoil or garden soil should have the right microbes to start it off.
I have to sift mine anyway. I made the mistake of putting it under a tree. And I put a lot of stuff that doesn't compost that well anyway, such as plum or peach pits or gourd shells. When I sift it, the stuff that hasn't composted goes back in. They seed it with the right microbes.
How do I layer it correctly so it will have success?
I'm not sure it really matters. It's going to break down anyway as long as you manage the moisture. It's a nature process and nature doesn't always layer it like the experts tell you too. Plus you lose all that when you turn it. I think the most important thing in making good compost is moisture control. Too dry and the microbes that eat it can't live an reproduce. Too wet and those good microbes die and are replaced by anaerobic microbes. These turn it into a stinking slimy mess. If it stinks the anaerobic microbes have taken over. Your nose will tell you when that happens.
Another important factor is the browns (carbon) and greens (nitrogen) mix. Too many greens can hold moisture and cause it to go anaerobic. This can happen even if your ratio is right but the greens are clumped together. If that happens mixing it up can really help. Even if your ratio of browns to greens is not perfect it will still break down, it just might take a little longer. Most of what you add is already a mixture of carbon and nitrogen, whether they count as brown or green depends on which is more prevalent. I found this bit of information that might help you. If you notice the experts don't talk about volume or weight, they talk about the number of atoms. No way can I keep track of that so I just make sure I have more browns than greens. It's going to work even if the ratio is not perfect.
All organic matter is made up of substantial amounts of carbon (C) combined with lesser amounts of nitrogen (N). The balance of these two elements in an organism is called the carbon-to-nitrogen ratio (C:N ratio). For best performance, the compost pile, or more to the point the composting microorganisms, require the correct proportion of carbon for energy and nitrogen for protein production. Scientists (yes, there are compost scientists) have determined that the fastest way to produce fertile, sweet-smelling compost is to maintain a C:N ratio somewhere around 25 to 30 parts carbon to 1 part nitrogen, or 25-30:1. If the C:N ratio is too high (excess carbon), decomposition slows down. If the C:N ratio is too low (excess nitrogen) you will end up with a stinky pile.
https://www.planetnatural.com/composting-101/making/c-n-ratio/
I scrape pure chicken poop off of my droppings boards. Pure chicken poop is highly green. If it is mixed with bedding the mix may be more of a brown, depends on the ratio of poop to bedding. If I get a layer of pure chicken poop on top of the compost pile it can draw flies that lay eggs and hatch out maggots. That's a good time for me to turn it, or mix the top layers or add a layer of dried grass clippings to cover it. If your chickens could get to it they'd love to eat those maggots and turn it by scratching but with your composter that may not be an option. If I had to do it over mine would be set up in the chicken run.
I don't layer mine on purpose to get better composting but it gets layered just by the way I put it together when I start. I have two bins, one where I collect stuff and one working bin. When I empty the working bin into feed bags bags after sifting I put in a layer of browns I've collected from the garden over time, usually things like dried corn stalks, sweeet potato vines, or bean vines. Then a layer of the stuff in the collecting bin in which includes the stuff I sifted out of it. Then another layer of dried browns. Then the rest of the stuff in the collecting bin. Then a layer of those browns, that finishes them off. I scraped the droppings boards that morning so next is a layer of pure poop. My last layer is dried grass clippings I've raked up. That kind of seals everything off and keeps flies and such off. Dried grass clippings are considered browns. Green grass clippings are considered greens.
After a week or two the microbes go to work and the pile really shrinks in size. So I scrape the droppings boards again and add a layer of pure chicken poop, then top that off with dried grass clippings. I may do that another two or three times as it shrinks in size to try to get more volume of compost when I finish, then start collecting stuff in the collecting bin for the next time.
I don't shoot for perfection in many things I do, I realize I don't have that tight of control over it anyway with chickens and gardening. I do the best I can and accept that as good enough. With composting I'm not going to try to count nitrogen atoms and carbon atoms. If it starts to smell I've messed up. It's too wet or I added to many greens, usually clumped together. Turning it enough to dry it out or mix it up usually takes care of it. Adding more browns doesn't hurt.
Good luck.
