I think you can only get through this if she is fully open to doing whatever you need to get that trust back. So if you think that counselling would help, then I feel she absolutely has to do it.
I'm worried that it sounds like you've put so much pressure on yourself to move on. Are you worried that if you keep the topic open too long you are going to lose her? It sounds like you are on the back foot her, whereas I'd be expecting her to be bending over backwards to show remorse and that she will do anything to earn your trust.
I feel like all the work has to come from her-not you. Even if you are questioning what you could have done to prevent this etc.
From a woman's perspective (and I'm so sorry to say this) I really don't think many women can just have sex with someone else when they are in a relationship.
We are talking stereotypes of course but women usually need some kind of connection or incentive to stray.
So either, she's craving attention/affirmation and has gone elsewhere (I'd stress this is selfish and NOT your fault!!) or she's considering your relationship and wondering what life outside it is like.
Whatever her motivation, there is more to it and I know it's painful but you really have to know the whole open truth before you can move on.
I really hope you can sort this out as you sound so invested in the relationship but I really think you have to enter this time with full acknowledgment that it may just not be possible to move on. If it is, the emphasis has to be on her-understanding why and her helping you learn to trust her again.
I agree with a pp that she hasn't tried to hide this, so the fact she's been quite blatant would make me question her commitment to you and resolving this issue.