Is it possible that I could be ready for a week of training?
It sounds to me like you are a beginner and have only started in boxing a week or so ago. If that is the case DON'T sign up to fight. A week or two of training is not enough time to completely learn the fundamentals and develop them to any real level of skill needed to actually fight someone else in the ring that has your physical destruction in mind. Any coach that would allow such a thing also is not your friend in any way. Once you get hit then everything will change in that ring for you in a bad way and you don't have the cardio for a three round fight unless you have been doing something else before this and have good cardio already. As a certified pro judge I donated my time to several promoters for amateur cards and judging them in kickboxing, Muay Thai, and MMA. I can't count how many times I would see a young person like yourself get into the ring or cage unprepared, untrained, and not in shape to handle what was about to happen and sometimes they would get hurt. Is this a sanctioned amateur bout? If so you need a license and to be registered and a requirement among others for that is that you have so much time training beforehand. Someone would have to falsify something for that then and there is a reason for requirements like that. If this is an unsanctioned bout just in your gym with another gym mate I would not recommend or support it either. There are all types in your gym and some will not have or show much mercy for you once the bell sounds and you find yourself overwhelmed and out of gas. Taking a fight of any kind should not happen for you before you have 3-6 months of training at least and maybe longer or not at all depending on how you react to taking a shot.
It would be crazy
Ready for a week of training, or ready for a bout after a week of training? Ready for a week of training, absolutely. Ready for a bout after a week of training? Not unless you're some sort of boxing prodigy, have had prior experience, or your opponent is a complete novice as well. Hopefully you're already fit enough to possess the stamina to get through three rounds should you decide to fight.
Depends how fit you are before that week. If you were completely out of shape a couple of weeks ago then it would be tough.