It's certainly not impossible. No one knows for sure if the universe is infinite or not. Let's assume, however, that it is infinite. Human beings are just a complex arrangement of atoms and speaking from a purely mathematical stand point, there's only a certain number of possible ways that atoms can be arranged. Somewhere out there, there's nothing stopping our arrangement from being repeated.
 If the universe is truly infinite, then that means that there are definitely people, actual people, who we could theoretically reproduce with somewhere else in the universe. In fact you, yes you, are just a complex arrangement of atoms and in an infinite universe any arrangement of atoms will be repeated. This means that somewhere way out in the cosmos there's another another you and another me and another anyone you've ever met. They could live on a planet exactly like ours and make exactly the same choices that we've made. On the other hand, maybe their planet is a little different or they're like us but they've made different choices, like a parallel universe but within our universe.
 With all that in mind, although there are only a finite number of ways to arrange atoms, the possibilities are vast beyond human comprehension. Probability dictates that any other humans out there will be so far away that the universe be dead before their light even reaches us. Plus, we still don't know if the universe is actually infinite which is the basis of this whole argument.
 You're absolutely right that a planet with similar conditions to ours could be out there. However, consider all the blind luck that allowed us to evolve. The asteroid that wiped out the dinosaurs, the layout of our continents, the fact that we have a moon, and so many more tiny things that indirectly led to us evolving. Any life that we may someday discover will most likely look nothing like us. That being said, if the universe is infinite, anything within the laws of physics that you could possibly imagine exists somewhere.