Should I let her go? Found baby pigeon

So I found one of my cats playing with this pigeon in one of the internal patios of my apartment. It seems that it has just left its nest and could not return. I looked for their nest on the roof and found nothing.

It has made a single yellow pasty poop and has not eaten or drunk (his crop is empty). What should I do? Should I leave it in a park and let fate take care of it?

I am from Peru, there are no pigeon rescuers in my area. I have 3 cats and I am afraid that they will hurt them.