count up in Column A until the next non-blank cell in Column C

Try

=IF($C3="","",SUMIF(OFFSET($A$2,MATCH(LOOKUP(10^10,$C$2:$C2),$C$2:$C2,0),0,ROWS($1:1)+2-MATCH(LOOKUP(10^10,$C$2:$C2),$C$2:$C2,0)-1),">0"))