I am not a physicist, but I was wondering what observation led to the conclusion that a particle can be at two (or is it multiple) places at the same time?
What do you mean by that "particles can be in more than one place at the same time?"
They cannot be so. Or, at least, no one has ever proved that happens, as far as I know. After a beam splitter, for instance, if you use a single photon you can consider it is using either one path or the other until you make a measurement. Then you find out which way did the photon really go through. In other words, particles do never use the two paths, but we usually say that it is as if they did so because until the measurement it is made, you can consider them to be in either one or in the other.