The only indication that openai is profitable comes from openai (whom I wouldn't trust with any statement, especially when it comes to profitability).
In fact there is evidence that inference is not profitable simply because the rate of losses doesn't seem to reduce as revenue increases: if inference had great margins, we would expect that as revenues increase, the amount of spend on training reduces as a fraction of total expenses. Since the loss-making fixed costs shrink as a fraction compared to the profitable inference, we should expect profitability to rise with total revenue.
However, all leaks of openai's numbers seem to suggest the opposite: as revenues increase so do the losses.