After Kerch I cannot see how it can be any earlier. Kerch bought the Russians valuable time.
If the POD is "no Tyfun" or "no diversion of additional Panzers to Leningrad" then it is possible. In some ways, this would be sensible as it stayed warmer in Ukraine allowing for campaigning.
The most sensible POD is that Hitler "sees the light" when the Panzers hit the mud OTL in mid Oct 1941. "Ah, my generals fail to see the 'big picture' and do not understand the economic aspects of war," he says. "Sevestapol is a dagger pointing right at the heart of the Axis, the Romanian oil fields. While there is still time, we must take Sevestapol and resume the attack on Moscow in the Spring."
He, not caring for rest for his troops, demands a "mad dash" for Sevestapol. It takes 6 weeks to move and refit (sorta) the bulk of AGC's armor down south. This coincides with Manstein's attacks and the timing of the Kerch Landings.
Though this does a number on German logistics and adds mechanical breakdown issues to much of the equipment, it ironically is less bad ATL than OTL. Much breakdowns occur where the Germans can retrieve the equipment and ultimately fix it, instead of lose it to the Russians. It actually leaves more usable equipment left over that is actually useful.
With this added amount of forces to the Crimean campaign, the additional armor deals with the Kerch landings and Manstein focuses solely on Sevestapol. The sudden set backs lead to a RUssian collapse and Sevestapol and the Kerch Peninsula are in German hands by the last week of December.
If this occurs the Axis still lose badly in a counter offensive from the Russians against the center. However, they would lose less equipment and less men, as they would be digging in and preparing defense. The Germans still won't be able to hold ground on the Don (as realistically if Hitler did this, he would see a mad dash to the East to secure Ukraine as equally relevant to the "economic aspects of war.")
However, Sevestapol would firmly be in German hands. It means Case Blue is launched a month early. Case Blue is only successful if this butterflies away Hitler's decision to take Army Group B's armor and send them south with Army Group A, which prevented Stalingrad being taken on the march.
It also means that the German's take their siege equipment and set it against Leningrad. Having not experienced the prolonged difficulties of taking Sevestapol, it may mean a larger attempt to take Leningrad. Likely, any savings in men and material created by the POD are tied down in Rhzev and in the outskirts of Leningrad.
I am not knowledgeable enough of German and Soviet capabilities to know what the effects of a hard drive at Leningrad, or surrounding Lake Ladoga in order to starve out the city, would be. If it is even feasible if the Germans save 20 divisions with such a POD. So, it could work out as a major win all around, a major loss if Hitler turns Leningrad into the new Stalingrad, or something totally different if Leningrad is real nasty and makes Hitler avoid the "rat war" in Stalingrad and hence avoids the late 1942 encirclements.
Lastly, it is worth saying, the moment the US is in the war Germany loses. All it does is affect how far West the Russians will get in the end.