Physical therapy should begin within a few days of the surgery. This is the most important aspect of your recovery. The surgery may not be successful if the therapy is not completed.
It is important to remember that the new ligament graft is still weak at this point in time. The bone needs time to heal around the attachment sites. The ligament itself will be at its weakest six weeks after surgery, after which point it begins to remodel and strengthen based on the stresses that are being placed on it in its new role as a ligament. It takes six months to a year for the ligament to regain full strength.
Even if you feel ready to play sports again a few months after your surgery, your new ligament is not yet ready. This is important to remember!