There are several people in this group that use Genesis Framework. Can you use Genesis and Beaver Builder together?
The place to start is page builders work best on a relatively blank full width page. Some theme systems such as iThemes Builder can easily make page layout and templates in any way you want – if for example you are going to use a page builder knowing that page builders actually are building in the Content area or another way of looking at this within the WordPress Loop. With Builder it is simple to just make a layout that only contain the Content module and make that layout full width.
With Genesis it is not that simple however there is a Genesis plugin Genesis Dambuster that allows you to create true full width pages which is what page builders need to work their best. Genesis and Beaver Builder gets into how to do this. Be sure to take a look at the example web sites. Dambuster also allows you to remove parts of the Genesis Foundation that you do not need or want.