Were Uthman ibn Affan and Alī ibn Abī Ṭālib alive at the same time?
Yes. Uthman ibn Affan and Alī ibn Abī Ṭālib were alive at the same time for 57 years, from AD 599 to AD 656.
Alī ibn Abī Ṭālib was 57 when Uthman ibn Affan died.
Uthman ibn Affan
Caliph of the Rashidun Caliphate from 644 to 656
Born AD 574–575 · died 17 June AD 656
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