This bit is the key to what Cal’s saying.
Yes, but read the 3rd paragraph of the same post. They lacked the resources
in theater. In June of 1944 the US had in the PTO:
48 APA (min 1,000 troops ea)
15 AKA
20 APD
3 AGC
9 LSD
186 LCI
135 LST
105 LSM
over 4,000 landing craft
Add the assets in the Atlantic (very few large ships, but lots of mid-sized landing craft that could handle a Med crossing) and yes, it is possible.
At least 10 fleet carriers (USS Saratoga CV03, Enterprise CV06, Essex CV09, Yorktown CV10, Intrepid CV11, Hornet CV12, Franklin CV13, Lexington CV16, Bunker Hill CV17, Wasp CV18) are theoretically available for planning purposes, and a few more (USS Ticonderoga CV14 commissioned 5/8/44 and USS Hancock CV19 commissioned 4/15/44) are working up. All nine Independence-class CVLs are available. Some 40 CVEs were in commission and worked up by that point, though many would be busy elsewhere. Figure 1,500+ carrier-based aircraft at a guess. 20 BB are theoretically available for NGF (12 old and 8 new).
The logistics would be a pain, but doable. Of course, the Germans couldn't fail to miss preparations on that scale and while the IJN was down at that point it wasn't yet out.
So it WOULDN'T have been done (ASB-level wouldn't), but it COULD have been done.