Hello!
Well, first of all, I do want to point out the obvious: solipsism is not a falsifiable hypothesis so proving it from a philosophical perspective would not make sens. But, if you are thinking of a physical perspective, than maybe you can do something with the double slit experiment. You could probably (I mean, theoretically speaking, I am not completely sure how to do this in real life) set a double slit experiment, where you have a recorder to track the slit thru which the particle moves, but the memory of the recorder can not be access. Something like, if you try accessing the memory, it self-destructs. In this case, if you look at the board where the particles hit and see an interference pattern, then you could say that consciousness is the basis of reality. That is because the information about the particles exists, but since no form of consciousness can access it, the particles still behave like waves. In this case, I would say that solipsism is correct. Otherwise, if you see bars, as if particles moved as balls and not as a wave, you would say that objective reality is correct, because information independent of consciousness decides the form of the particle movement. If you like my response, I could try and figure out the details of the experiment, but to actually do it in real life is really hard. From what I know, setting up a double slit experiment costs around 100K. Sooo... yeah.