Is it plausible that we could be related to everyone on the planet? Let's talk about ancestors. Four generations back, the number of your direct ancestors (parents, grandparents, great grandparents) total to 30 different people. If you continue with that math for forty generations back (and doubling the number to include both maternal and paternal sides), the math looks like 2^40, which comes out to 1,099,511,627,776 direct ancestors. That accounts for more people than have ever even been alive (that number is a mere 107 billion people)...which means the math doesn't add up. So what's the glitch? Inbreeding.
Because so many people with shared ancestors have reproduced, the number of actual ancestors is much smaller than the simple math would show. But using more complex mathematics and factoring in all sorts of aspects regarding human migration and life expectancy, we have determined that everyone alive today shares a common ancestor in their family tree - someone who lived roughly 3,000 years ago and essentially spawned all of us here today.
How do we know that? Scientists are able to use DNA as molecular clocks to determine how much time has passed, while also determining how related humans are based on the common changes in their DNA. Furthermore, based on analyses of mitochondrial DNA, we know that we really are all one big family, with all of us descending from one woman's mitochondrial DNA who lived about 150,000 years ago in Africa. So what's our collective mama's name? They call her Mitochondrial Eve!