Being in good physical condition is the best medicine to avoid altitude sickness. That, keeping hydrated and getting enough rest. Traveling from sea level to the site and going out on the first day is asking for trouble. There is only 2/3rds the amount of oxygen in the air at 10,000 ft. a there is at sea level. Your body will eventually manufacture the hemoglobin so your blood can carry more oxygen but it takes time. Giving your system an extra day with plenty of rest will give it a chance to acclimate.
The other thing you can do to help, with your doctors advise of course, is to get a good aerobic exercise program and push into the anaerobic level briefly. Running is great for that. If like me your knees can't hold up to that any more, lap swimming will do the same thing. Your body will sense the oxygen debt and start building more hemoglobin before you go on your trip. I'ld find a good trainer to help you. You should be able to find someone at local fitness center.
Get in shape! Not only will it help prevent altitude problems, but you will enjoy your trip much more if you are not sick or struggling to keep up.