I think you're confusing what "looping" means. It just means that whatever is happening at the end leads to the beginning, in a way that you can't tell where the thing starts or ends. So you can make it loop with the particles fading out, moving, growing etc. That article I linked to has an example of the looping smoke…
There's a great article in here: https://simonschreibt.de/gat/fallout-4-the-mushroom-case/ They mention baking a smoke loop but don't say how it could be done, so that's still a problem. They do link to this other article that talks about looping using a combination of static textures:…
I don't use Maya, I hope someone else can help you with the software-specific. In any case, I'd try rendering an image sequence using an orthographic camera, using a translucent material for the fluid or smoke. You should find some Youtube videos or the Maya docs to see how to do that. The output format should be 32-bit…