I would do it with something that way, starting from a date and adding N weeks period to it
my_data <- data.frame(year = sample(c(2018,2019), 100, T),
week = sample(1:52, 100, T))
#> Attachement du package : 'lubridate'
#> The following object is masked from 'package:base':
dates <- make_datetime(year = my_data$year) + weeks(my_data$week)
#>  "2018-10-01 UTC" "2019-03-26 UTC" "2019-06-11 UTC" "2018-07-02 UTC"
#>  "2019-05-28 UTC" "2018-08-20 UTC"
Created on 2019-11-14 by the reprex package (v0.3.0)
Just take care of week numbering and start day of the week maybe.
Does it makes sense ?
Otherwise, when parsing character to date I think there is a
%W available to describe week format. Look at
Hope it helps