The code below should give you a new vector with the values in date converted to numeric dates.
dateNew <- as.Date(date, format="%d %b %y")
Here is a reproducible example with a small version of your date variable.
date <- factor(c("01 Jan 19", "02 Jan 19", "03 Jan 19"))
str(date)
#> Factor w/ 3 levels "01 Jan 19","02 Jan 19",..: 1 2 3
dateNew <- as.Date(date, format = "%d %b %y")
str(dateNew)
#> Date[1:3], format: "2019-01-01" "2019-01-02" "2019-01-03"
dateNew
#> [1] "2019-01-01" "2019-01-02" "2019-01-03"
Created on 2019-11-13 by the reprex package (v0.3.0.9000)