This is very, very likely, and there's even concrete evidence, based on the fact that the human race was nearly wiped out 70,000 years ago, but recovered.
70,000 years ago a huge volcanic eruption with global consequences called the "Toba event" reduced the human population to somewhere between 3,000 - 10,000 people. We know this by analysis of our DNA, which carries a lot of information that can be used to assess our genetic history. That record shows that a severe genetic bottleneck took place 70,000 years ago, and geographic evidence shows a corresponding massive volcanic event thought to be responsible. More here: