x <- c(NA, NA, NA, 6, 5, 3, 7, 2, 7, 8)
y <- c(NA, NA, NA, NA, NA, 3, 5, 6, 3, 9)
z <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
mydata <- data.frame(x, y, z)

for (j in 1:ncol(mydata)){
index[j] <- min(which(!is.na(mydata[,j])))}

Position(function(x) !is.na(x), mydata)