if you already have dragons and orcs and elves, and people with no DNA put in place by Gods, it's not going to stretch credulity to have black people.
But sure, let's ask a couple of questions about this.
Are darkskinned people from other regions? Or are they simply part of the setting because of the God placement thing? All you really have to do is mention various skin colors and types of folk, in either case as part of the setting. If they are from elsewhere, then they have to have had a means to travel to these other regions much earlier.
I don't have a more in-depth answer than that and, quite honestly, I can't think how that is more wild and unbelievable than orcs.
EDIT: Since it isn't Europe, just go ahead and make dark-skin the default and white skin odd. Why the heck not? Just make it Black Not!Germany. All of the beer steins and none of the pasty-whiteness.
EDIT: Marky's comment has inspired me. Some of the people should be blue. I think that would be fantastic! Again, why not! We do have blue people right here on earth! But hey, there's an actual matter-based reason for that, so we can say one of the gods did it to a group of people. I love fantasy. Anything is possible. Dragons and blue people, coming together! (Not sarcasm!)
EDIT: The OP's edit has dashed my dream of blue Not!French folk running about. Black Not!Germany still stands though. See you or someone else edited it from Europe to Tolkien. The rest of my answer still stands. Just don't be nervous about it. Make your world. Tolkien was racist, sexist and used Europe as his model and he still had the occasional brown skinned person show up. In the background. Far away from the main characters. The very white main characters. Meanwhile, the other more evil, lesser races were given physical descriptions that could be applied to black folk. Here's a link to a fairly balanced article from the Tolkien Gateway regarding that. For his day, I think he was a fairly decent person, but because of his example and because everything is Euro-centric, I guess that has caused you to ask if in a world of Dragons, orcs and halfings, if black people are allowed to be there, even if there are no laws of physics. You, as the writer, are aware that this is so ingrained in the culture of fantasy. I think this question means that there's such a white cultural bias in fantasy writing, that it's now more unbelievable to have a black person in a story than it is a dragon. Please make your MC brown. I beg this of you.