Peter never hesitated to take the lead, he was led by the Holy Spirit to do so. History confirms Peter as the first pope even if he himself did not see or understand that as his role.
One must understand that though they were the first Apostles and the first disciples, they did not know everything. We see in Acts how questions came up, then the Apostles gathered and a decision was reached on how to handle or answer these situations.
That dynamic has not changed in the Church since its beginning.
Please enlighten me. I am not aware of hard, factual, history which confirms Peter as Pope.