How to plot multiple lines on the same plot without adding traces

I am trying to plot random points in a sphere. Then I am trying to connect every point with the origin.
My approach is to generate random points in a sphere and plotting them in one trace. I am then adding traces in a for loop where each trace is a graph of one line connecting a point to the origin.
So if there are 500 points, there are 501 traces (one for plotting points, and the other 500 for lines), which I think is taking up a lot of RAM and causing my computer to crash.

Is there a way to plot multiple lines without adding a whole lot of traces?