Your challenge is to come up with a plausible POD to turn a Sherman tank into a Sturmgeschütz type vehicle. Perhaps WWII has dragged on longer...
Maybe...
Winter 1940:
The British are desperatly shopping for armour. They have heard about Soviet self propelled guns and are interested in them for the same reasons as the Soviets. Not satisfied with the Lee tank, they request drawings of an infantry support tank on a Sherman chassis. They, will of course, want the turrented Sherman as well
-Its cheap (in early 1941, lend lease put more emphasis on lease)
-It fits well with the British infantry tank philosophy of cruiser tank / infantry tank mix
-Its easier to maintain that an turrented vehicle and can be used more readily by new crews
-There are still jitters of a German invasion possibility and a more heavily armoured defensive tank could come in handy
1941-42:
The British take delivery of about 1,000 sherman stugs. The British use a few in manuver armoured regiments, but most are used as infantry support or in engineer units. Not facing a manuver threat and impressed by the frontal armour, the USMC requests several hundred Sherm stugs as well.
1942-45:
The U.S. and British interest in the stug variant declines. But... the eastern front consumes armoured vehicles at a horrendous rate, more than even the Soviets can produce. The Sherm-stug, but not the Sherman is offered to the Soviets. Paranoid U.S. armaments officers congratulate themselves that the Soviets will not get the the U.S. lead tank (little do they know that the Soviets have far better tanks of their own). Thousands of Sherm stugs are delivered to the USSR.