During the interview, the Anglican leader was asked what he felt about famed physicist Hawking's recent declaration that "there is no Heaven or afterlife" and that it is all "a fairy story for people afraid of the dark".
Sentamu first made clear, "I'm not afraid of dying. Bring it on any day."
The Church of England cleric continued, "[Hawking] shouldn't paint a picture of some kind of sky stuff up there because the faith of God is not that kind of faith. The coming of Jesus in human flesh on earth was actually trying to say, 'when I look at you ... you should be telling me more about what God is and about what it is to be human'."
Sentamu told the BBC that he would tell "that wonderful professor" not to picture another image which most people do not have at all.
Observing that Christianity had to contend with not only views from people like Hawking, but also other religions as well, the BBC asked what the challenge was for believers.
"The challenge really seems to me is not to try and think that we're in the marketplace where we're all looking for an easy bargain," Sentamu shared.
"Where we are is that, God becoming human in Christ was trying to say if you want to know the authentic human life it is lived in a man called Jesus and if you want to know God, it's not some kind of imaginary power out there.
"[God] actually takes upon our own nature so that we would become more loving, more caring and in the end, God for me is Christ-like."
He added, "If we do the will of loving and caring, of supporting, of rejoicing in the fact that human beings are made in God's image and likeness, I think that's a great thing to be done.
"So living with people with other faiths, I'm not so much pushing my idea to them, I'm more called to be loving, to be caring.
"It doesn't mean I shouldn't tell them about God by the way [but] I should be caring that in what I'm saying, I myself completely believe in the reality of the God that I've seen in the face of Jesus Christ."
Nevertheless, the Anglican leader believes the world would be a better place if people talked about God as much as they did the weather.
"If [people] talked about God in the same way that they do about [the] weather we may be in a very different place," he told BBC.
Sentamu's two-day pastoral visit to the Diocese of Sheffield included a visit to the All Saints Secondary School in Rossington, Doncaster College and the Young Offenders' Institution.
Holding a question and answer session with the inmates at the institution and with the students at the Church of England School was the highlight of his tour, he said.
He also toured the Archer Project, a day centre for the homeless and vulnerable on Thursday and met with business leaders and over 850 workers in Sheffield, touring Forgemasters, a 200-year-old steelworks led by chief executive Graham Honeyman and non-executive director Peter Birtles.
"We were delighted to hold this historic visit for the Archbishop and his senior colleagues and provide an insight into the steel heritage of Sheffield and the wider world of manufacturing," Birtles said.
"All the clergy seemed to have thoroughly enjoyed hearing about the history of Forgemasters with Dr Sentamu spending a lot of time talking to the various members of staff and in particular the apprentices and listening to their achievements and experiences here."
The Bishop of Sheffield, Dr Steven Croft, relayed that his aim for the Archbishop's visit was "to give the Archbishop an idea of some of the issues affecting people's lives in the Diocese as well as celebrating many things [they were] deeply grateful for."
Sentamu told BBC he hoped his visit to Sheffield would tell people that the Church was present throughout the area and that the doors are open for other people to enter through.
"The joy for me in the Church of England is that there isn't an area that the church doesn't cover."
He praised the churches in Sheffield as well, noting that they were genuinely invested in helping their neighbours.
"If you look in Sheffield, there are churches out there who are trying to help their neighbors. These people really aren't just doing it because they want more people in their churches, they're simply doing it because they want to tell other people about the love of God."
The visit came to a close after Sentamu attended the Cutler's Feast in the Cutler's Hall.
"We all need to play an active part in our communities but the state also has a role in helping to fund, support and encourage projects," he said.