Overpopulation is a result of a country's crude birth rates (CBR) being higher than its crude death rate (CDR). In your question, you listed an option of CBRs soaring (birth rate soars) which could be a cause of overpopulation but if a country's CDR is high enough to equalize or overpower the CBR then it is not the right answer. Given more context, you can determine if that is the right option or not, but in my perspective I am going to rule out that option.
Therefore if you use the concept of how CBRs and CDRs work then the best answer I would have with your given context would be when the CBR exceeds the CDR. ("birth rate exceeds the death rate")
Hope this helps
