R crosstalk: how to set default values in filter_slider() in order to filter date column

Question

My question is similar to this question, which asks how to set default filter selection in crosstalk::filter_select in R. However, I need to do the default select for crosstalk::filter_slider for a date column. I have created a reproducible example with dummy data, filters and working default selection for the categorical filter. I would like to be able to do something similar for the date slider. How should I change my JavaScript so that, for example, the date range between tomorrow and the date after tomorrow is selected?

library(crosstalk)
library(htmltools)

# dummy data
dat <- data.frame(
  date = Sys.Date() + 0:4,
  letter = letters[1:5],
  number = 0:4 + 1
)
# shared data
dat_shared <- crosstalk::SharedData$new(dat)

# custom js (contains unfinised code for date filter!)
custom_js <-   shiny::tags$script('
    // this is not complete and it does not work
    function filter_date(){
      document.getElementById("date")
    }
    $(document).ready(filter_date);
    
    
    // this is an example how a default selection can be done using JS which works
    // it selects a for the filter (the default is that nothing is selected)
    // I want to do something similar, but for a date filter
    function filter_cat(){
      document.getElementById("filter_cat").getElementsByClassName("selectized")[0].selectize.setValue("a",false)
    }
    $(document).ready(filter_cat);
    '
)

# filters for the widget
filter_cat <- crosstalk::filter_select(
  "filter_cat", "Select a letter",
  dat_shared, ~letter, multiple = F
)


filter_date <-  crosstalk::filter_slider(
  "filter_date", "Date",
  dat_shared, ~date
)


# showing the widget in RStudio
htmltools::browsable(htmltools::tagList(
  custom_js, filter_date, filter_cat
))