An 8-month-old boy is brought to the orthopedic clinic by his parents with a complaint of asymmetric gait and a limp that has been noticed for the past 2 months. The child was born in a rural area and did not receive routine screening for hip dysplasia. On examination, there is a positive Trendelenburg sign on the left side, limited left hip abduction (45 degrees), and a shortened left lower limb by 1.5 cm. X-ray of the pelvis shows a high acetabular index (>30 degrees) on the left, with lateral displacement of the femoral head. What is the most likely diagnosis and the primary goal of treatment at this stage?