Were Alī ibn Abī Ṭālib and Aisha alive at the same time?
Yes. Alī ibn Abī Ṭālib and Aisha were alive at the same time, from AD 614 to AD 661.
Alī ibn Abī Ṭālib was 14 or 15 when Aisha was born.
Alī ibn Abī Ṭālib
4th Rashidun Caliph (r. 656–661) and first Shia Imam
Born 17 March AD 599 · died AD 661, aged 61 or 62