I managed to figure this out. Here is what I ended up using for those interested.

=BYROW(INDIRECT("C3:"&ROWS(A:A)),LAMBDA(x,IF(INDIRECT("A"&ROW(x))="","",COUNTIFS(x,">"""))))

I'm not sure if there is a cleaner or more efficient alternative but this seems to accomplish what I needed. I will refrain from choosing my own answer until I hear from others.