I had this question a while back (
https://www.alternatehistory.com/forum/threads/plausibility-check-aishas-caliphate.504433/). The scenario I came up with was one where there Aisha wins at the Battle of the Camel, with a death of Ali and his sons, but al-Zubayr and Talha still die. Abd'Allah ibn al-Zubayr and other Quraysh then rally around Aisha in order to stave off total dominance from Muawiyah.
However having done more reading the problem is that Muawiyah is simply not a big enough boogeyman in order for this to work. You need a real existential threat to the Ummah in order for Caliph Aisha to become anything more than a fringe proposal. A more likely scenario is where Aisha forms a political alliance with another candidate and acts as the power behind the throne.
If you really want Aisha to be Caliph you need to get close to ASB territory. You could have the Battle of the Camel prove much more deadly to the senior leadership of the Quraysh (people who weren't even involved in the OTL battle need to die) and then Muawiyah, supremely confident in his position without any serious rivals, makes an extraordinarily large blunder by declaring himself a prophet on equal status with Muhammad. This idea is palatable amongst recent Syrian Arab converts who are used to ideas of semi-divine kingship in the Persian tradition, or palatable enough that Muawiyah isn't immediately knifed in his sleep. He begins a march down south to assert his claim to Prophethood and a panicked, leaderless Qurayshi coallition nominates Aisha as their Caliph.