@Fabiola87 Explain the situation with the Customer Service agent. Show the communications (which hopefully, you have done through the message thread.
If a guests arrives at 1:50am, which I assume is way past your check-in time, G has no right to enter your premis without prior approval. If the guest left, without discussing this first with you, Airbnb must honor your payout as it was the guest who is at fault. Any possible claim from a guest must come after the guest has first intended to communicate with the host to try to come to a mutual agreement. If the guest did not do this, Airbnb cannot (and I believe they will not) take the guest's word for what occured.
Make pictures of the damage and proof of break in so you proof this and you can claim property damage costs.
I hope this helps.