The review concluded:
To date, there is no evidence that hyperbaric oxygen therapy improves core symptoms and associated symptoms of ASD. It is important to note that adverse effects (minor-grade ear barotrauma events) can occur. Given the absence of evidence of effectiveness and the limited biological plausibility and possible adverse effects, the need for future RCTs of hyperbaric oxygen therapy must be carefully considered.
This really suggests that further research is likely to be too risky.