Can I bake a cheesecake using only a water bath?

There are a number of technique that you may find acceptable as alternatives to an oven, it in part depends on what equipment you have available. Any of these technique have their champions and recipes can quickly be found with a web search.

Try "stove top cheesecake" and you will find recipes for using a covered frying pan for instance. I personally have tried and those are not my favorite, at least of the one I tried as I found it difficult to control temperature. Here is a blog recipe with an example of this type of technique. It is not actually the one I have tried and no promises on the actual recipe, but the point is more the technique and a starting point.

Dutch oven I have not tried, but that seems like a very promising approach if you have one as it would trap steam while acting as an oven. I may have to try it in fact. I consider the pressure cooker to be a sped up water bath, and a covered dutch oven to be not far from it. Covered, a straight water bath could be very similar but take longer while these options would up your temperature and speed the process. This is a Scouting Magazine article on the Dutch oven method. Again, I have not tried this one, nor do I endorse the recipe, but the method seems very adaptable and with the way a dutch oven works, I would think it will work well. I know how nicely it creates a steam dome for breads for instance.

I personally have had very good luck with an instant pot, and most any pressure cooker would work for those recipes. If you have one, that is an option worth trying and seeing if you like the results. It will not get you a browned crust top which some people prefer, but I have found it easy to adjust between a bir more moist to a drier result according to taste. This is for pressure cookers/InstantPots. There are many similar out there and this is one I have gone my before for technique. Most any cheesecake recipe I have used would easily adapt to this, I went there for just the ideas and timing. With pressure cookers, some recommend enclosing in foil, some not. I have found it does not make a lot of difference as long as you lightly remove any condensed water as soon as you remove from the cooker and before if fully sets. I have liked my results, but of course it requires a pressure cooker.

As I consider for applications like this a pressure cooker to be a pressurized water bath, by extrapolation I would say you could do stove top water bath for the entire process, but would have the disadvantage of it taking longer.

Those are a few options over an oven. The dutch oven technique is championed by campers as well which is shouting at me to try next summer. Each of these I just picked one item out from search results and there are many more examples that will pop up in any search engine. For myself, I have found methods like the pressure cooker to me more forgiving and more available for experimentation than oven baked to be honest and it produces what I consider to me a real and tasty cheesecake.