dump $variables in theme_preprocess functions
The best way would probably be a breakpoint with xdebug turned on. Which requires configuration efforts though.

What I was normally doing in similar cases was a step-by-step approach. I was printing out $variables keys first and then narrowing my var_dump with a specific key. E.g. var_dump($variables['key']). Slowly but surely.

In the end I think that in terms of efforts it is way better to set up debugger and use breakpoints to inspect variables.