The carrier inventory that actually existed in early 1939

Did Japan already possess enough carriers in 1939 to match the British and American coalition?

No; Japan had about two fleet carriers and one light carrier, while Britain and the United States together could field a much larger carrier force, especially after Kaga's loss.

Several Japanese carriers familiar from the later Pacific War were not yet in service in early 1939. Japan had roughly two fleet carriers and one light carrier before the counterfactual loss of Kaga. Britain could bring four to six carriers and the United States another three in the coalition scenario. Exact deployment would still take time, but the opening balance cannot be calculated from Japan's later wartime inventory. The January 1939 crisis has to be assessed with the smaller force that existed when the scenario begins.