The image (after removing ALL clipping masks and groupings) was made of black lines. They are not joined together, so there's no closed areas to be filled. I show the construction idea of the image by recoloring a few lines:
The white fill is possible:
- Make a copy of the original to the clipboard
- Select all, apply Path > Stroke to Path; it converts all lines to filled areas with no stroke (takes a long time).
- Select all, apply Path > Union; you get a complex black shape with holes
- Select all, apply Path > Break Apart; this separates the interiors of the holes
- Select all, apply Path > Union; you get one shape which covers the original. It's black:
- Change the fill color to white and paste in place the original:
BTW. I got a PDF when I opened the link you gave. Poppler-Cairo import opened it easily. I removed all groupings by applying Extension > Arrange > Deep Ungroup. This time it hadn't much to do. Some PDFs can have 50 levels of groupings.