Were Alī ibn Abī Ṭālib and Fatima alive at the same time?
Yes. Alī ibn Abī Ṭālib and Fatima were alive at the same time, from AD 604–615 to AD 632.
Alī ibn Abī Ṭālib was 33 when Fatima died.
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