Not really - give any reasonable sized group of humans a few thousand years and it happens automatically.
However that's not what you meant! I think the answer is yes, though I've never tried. If I were going to I would start in the same ways babies learn to speak - with single words for common objects in their surroundings. Things that are very common may have words for different types (e.g. innuit and their words for snow). Then I would develop how to indicate something in the future as that allows planning of hunting / agriculture. Then how to indicate the past since that allows reverence of ancestors, which most cultures do in some way or other, and the ability to learn from the past. It is also the typical tense of stories, so would happen early on for nights around the campfire. As the culture expands it will encounter new things and so it's language will expand in parallel. You can have words for concepts that current languages don't have such as 'the tension in a wet bowstring' v 'the tension in a dry bowstring'. I would guess those kinds of nuances will make it come alive rather than leave a reader thinking "Why not just use english?" (or whatever other language you write in). If you plan to use it only for names, then getting as far as the words for common things may be enough - many place names are essentially descriptions of local features in some language or other sometimes with the name of a chief attached.
There some good books on Conlanging out there. A full-blown language is not easy unless you're gifted in the field. Naming languages and simpler manifestations of conlanging are easier and take less time and dedication.
I think unless you’re already a linguist, you’re going to find it a struggle. Just my opinion. On what are essentially made up words for the purpose of fantasy writing, I’d say that’s more in the region of entirely doable, you would just need to be pretty exhaustive when it comes to etymology so you don’t make up a word that’s inadvertently an obscure slur in another language. You would also need to be super consistent too.
In the past, I found I only needed to create enough words to create the illusion of a language underneath, but in writing, it was just distracting. Popping up words with no translation that no reader would bother to try and sound out. It did not really have the immersive feel I was thinking it might. I did try to create a dictionary to it though. Keeping track of root words and what might mean what to use it again when needed. But...it was not worth the effort.
In my current tale, there are so many languages flying around, it would be mind numbing to try to make each sound like a language. I think I have somewhere like 14-15 floating around at the moment.