For adding the values in the pre-existing data table, you can just apply the paste0 to add the day to the character and then use the as.Date to control it:
DT[, dt_start := as.Date(paste0("01/", DT$dt_start), "%d/%m/%Y")]
The result of the above command in R programming will be:
DT
n dt_start
1: A 2020-10-01
2: B 2015-05-01