How to make a VGA monitor display a white screen at all time?
It's not a simple wiring job unfortunately.

Like armandas said, you'll need to put 0.7V down the R, G, B signals, which seems easy. However, in order for the monitor to come out of suspend and display an image, you must also provide valid HSYNC and VSYNC waveforms.

You'll also need to turn off the display (so, 0V down the R, G and B lines) when either HSYNC or VSYNC are active.

To do all this, you'll need a clock generator (around 25 MHz for 640x480), two counters (one for horizontal position, one for vertical position), eight comparators (four each for horizontal/vertical), and some glue to combine the results.

But then your troubles are just beginning, because you've just made the timing generator of a raster graphics display. There's lots more work ahead of you before finally digitising, rasterising and displaying an oscilloscope signal on the CRT.

It's likely that one of your best options is to use one of the CRT display controllers suitable for microcontrollers. Some solutions are described in this question.

You should look at this question too, because it's pretty much identical to yours.