Is there a way to create a count of nonblank cells within a matrix based on columns header and row?

I have data currently formatted like Table 1 below. I need to create a formula to populate the matrix in Table 2. Essentially I need to count the non-blank cells if the column and row match. There are duplicates in the columns so I need to aggregate these together. I already have the rows and columns of Table 2 created. Any ideas on the easiest way to do this? I already tried a mix of counta and countif formulas without any luck.

Table 1

Table 2