Do think it’s possible that that some people can be born without a conscience?
I think everyone is born with a conscience. In Romans 2:14-15 Paul wrote, “Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law, since they show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them.”
As to people who appear not to have one, Paul said some people’s consciences have been seared as with a hot iron (1Tim 4:2). By this he meant that over time, after repeatedly ignoring their conscience, some people can acquire the ability to behave as though they don’t have one. People like this are sometimes described as being sociopathic.