Japan is far enough from Okinawa to make CAS a challenge. Fighters would need drop tanks instead of bombs and would not have much loiter time. I guess that P-47N's could have handled it but not much else.
Okinawa to Kyushu about 400 miles. Kyushu to Tokyo about 600 miles.
CAS in the early days of both Operation Olympic (invasion of Kyushu planned for 1 Nov 1945) and Operation Coronet (invasion of Honshu planned for 1 March 1946) would have been a USN responsibility.
The US Fifth Fleet, responsible for making the landings for Olympic, was to include some 36 CVE both to protect the various forces on the approach and during the landings, and provide CAS once the troops were ashore, just as they had done in previous Pacific landings but on a larger scale. Those would have included about 8 of the big Commencement Bay class with USMC air groups specially trained for CAS.
Those carriers are in addition to 5 USN fast carrier task groups assigned to 3rd & 5th Fleets (14/15 CV + 6 CVL) plus 2 task groups from the BPF (4/5 fleet carriers + 4 light fleet carriers).
The objective of Olympic was to grab real estate for airfields to help support Coronet. It was only intended to take the southern part of Kyushu to achieve that. Once successful landings had been made, airfield construction could begin immediately and USAAF & USMC units begin to move in.
It is worth bearing in mind how things worked during Operation Overlord. Emergency strips opened within a couple of days, rearming strips a few days after that with the first units moving from southern England within a couple of weeks or so.
Edit:- Same thing happened in the Pacific with the landings on Leyte and Okinawa. Leyte landings 17 Oct, first USAAF units moved into reconditioned and expanded airfields from 24/25 Oct. Okinawa the first USMC moved into Kadena 9 days after the invasion.
There were at least 13 Japanese airfields and landing grounds in southern Kyushu in the immediate vicinity of the areas of the intended US landing beaches. USAAF close support depends on how quickly these could be captured or other sites identified and turned into airfields.