Is possible to detect the problem with the knee by doing orthroscopy immediately after injuring it.

Yes: Yes, a knee arthroscopy is probably the most sensative way to determine if the internal structures have been injured. The reason we don't usually do a knee scope to make a diagnosis is because there are many noninvasive ways to detect injury and many knee injuries do not need surgery. So a physical exam, X-ray, and possibly an MRI go a long way in finding the diagnosis before surgery considered.