America is a fruit salat of diffrerent christian ways, Mormons, Baptists and so on, while most european countries stick with the traditional Catholicism or Evangelicalism, meaning many people in Europe have become atheist/agnostic.
Earth is 4,5 billion years old, remember, if this "Random chance" happend over 9000 times every femtosecond, it wouldn't take long for you got the result you want, please come with more information if you want your case fleshed out.
Plantmen are cool.
But sadly they are good food for bugs and mammals (Mice, Rabbits, Hares, ect), and remember, bugs and mammals also evolve. That 'soon' will turn into a plantman after millions of years of evolution, And if plants don't find ways to protect themselves against the new bugs and mammals, they will die out.
Plantmen are never going to happen, sorry, there are also billions of other ways it will fail, but I ain't got time fo dat.
But there is a second way complete your dreams, MUTATIONS! Recently, a snail that lives under water have been discovered, it eats plants, and keep them in their belly, so they can produce oxygen to them, pretty cool right?
I know I wrote this very murky and unclear, but if you understand the basics of Evolution, you know where I'm going