Is there scientific (observe/test) evidence that any known phenomenon can produce (none existed before) information besides intelligence?

Yes, the information contained in an oxygen atom to join with two hydrogen atoms to form water. And then that water has the information necessary to dissolve sugar cubes which neither had before. And then the water evaporates and the sugar has the information to form the lattice work of crystals. Or how a ball knows how to roll down hill.

Not sure exactly what you're asking. Are you asking the old can "something" come from "nothing" question? Yes, look up quantum vacuum fluctuations. They happen all the time, all over the place. It's when energy just randomly pops into existence for no reason, out of nothing, with no cause.

DNA contains genetic information. Microbes have DNA but they are not intelligent

Is this like a 'if a tree falls in the forest an no one is around to hear...' question...?

Your weird use of the word information makes me think you are a creation doofus.