Welcome to SI Wolfpack1.
A few small things. First, I see that you registered back in August. While I'm sure the past few months have been difficult for you both, you should be aware that recovery from infidelity is something that takes... time. Years. We often estimate around 2-5 years of recovery before R can even really begin in earnest (and even then, things such as "trickle truth" can reset the clock back to zero every time it happens). I say this simply to set an expectation in your mind. The first year or two is often volatile and difficult even under the best of circumstances. So set your sights accordingly. You wouldn't expect to be jogging again a week after breaking your kneecap, and you shouldn't expect trust to be regained just months after infidelity. Setting an impossible standard for yourself and your spouse will only lead to more frustrations.
One of the traps we WS's tend to get ourselves into is thinking that there is something we can do, or say, to make everything better again. It doesn't work that way however. Imagine that someone mugged you, stabbed you, and left you for dead. Would you trust that person more if they made a really heartfelt apology to you? Probably not. Which leads me to a question for you... when someone apologizes for something they did, who do you think they doing it for? In other words, are they apologizing in hopes that it repair the damage done to the other person? Or are they hoping it will absolve them, and make themselves feel better?
As you already said, she does not, and cannot, trust you. You were the one person who was supposed to "have her back" no matter what, the one person she could trust to never hurt her, or lie to her. And yet, you did all of those things, and more. Her entire world was pulled out from under her, and now, if the person she was supposed to trust the MOST in this world could betray her and lie to her, and "stab her in the back" instead of guarding it, then how can she trust anyone or anything ever again? This is so much larger than trusting you. Her entire sense of trust is shattered. She doesn't trust you, she doesn't trust anyone else, and she doesn't even trust herself at this point. You are focused on her trusting you again. She's focused on the fact that she can't trust anyone or anything. She's simply not in a position to trust you right now, and to be honest, you've given her only the most minor of reasons to do so.
(Just to be clear, I'm not trying to attack you or make you feel badly here. I'm a WS too, as are most people here in this forum. We get it. We've been where you are, did the same things, thought and felt the same way, and made the same mistakes. My point isn't to berate you. It's to help push you into another, more helpful, point of view).
Imagine for a moment that a drunk driver hit you with their car. The driver gets out, says "Sorry", and then asks if you forgive him and will help him fix the dent your head left in their hood. Have they done enough to earn your trust back? Do you get the feeling they are really concerned about your welfare?
Now imagine that the driver instead rushes out and checks on you. He calls 911 right away, and rips his clothes and uses it to bandage you up. He covers you up and helps keep you safe while you wait for the ambulance, and he assures you that he will take care of all the hospital bills. While you recover in the hospital, he checks on you daily. He offers to pay your rent and bills while you are healing up. He joins AA, gets clean, and makes a pledge to you to never drink again. He sees an IC and gets help to understand his addiction and his impulsivity and to treat them. In short, he does everything he can in order to both take ownership of what he did, do his best to help you in whatever ways he can, and takes steps to change himself at his core so it will never happen again. Now do feel he is really concerned about your welfare?
My point is, it's not about what we say, or even really what we do, it's more about "who we are" and how we hold ourselves accountable. Most of us would be more open to forgiving someone who bends over backwards to change and own their mistakes, then we would be to someone who simply apologized and felt badly. Feeling badly is about THEM. Doing something about it, is what we need to see. Words without actions and meaning, are worthless.
As others have said, write a timeline, take a lie-dectector, whatever she wants, but at the end of the day, what will help her the most is to see actual empathy from you, ownership, and change. She will consider trusting you when you give her a REASON to do so, and not a moment before (if at all). For now, work on understanding your "why's". Why you cheated is a long, complicated question that will amount to more than, "Because I wanted to". Figure out what in your life made it okay to cheat, what you actually hoped to gain (other than sex), and why you allowed yourself to debase yourself in such a manner. That's where to start. Once you understand why and how this came about, you can take steps to change.