Were Umar ibn Al-Khattāb and Alī ibn Abī Ṭālib alive at the same time?
Yes. Umar ibn Al-Khattāb and Alī ibn Abī Ṭālib were alive at the same time for 45 years, from AD 599 to AD 644.
Alī ibn Abī Ṭālib was 45 when Umar ibn Al-Khattāb 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