Preventing some some elements from being `sample()`ed in a for loop

My for loop below uses elements in time_to_remove to remove them randomly a study. The available elements of time to remove are: 2, 3, 4.

But there is little issue. time elements have an order. So, after sample()ing for removal, we can't end up with: time = 0,1,3 or time = 0,1,2,4 etc. We should only end up with: time = 0,1, time = 0,1,2, time=0,1,2,3 or time=0,1,2,3,4.

I wonder if such a condition can be added to my current code below?

library(tidyverse)
data <- expand_grid(study=1:4,group=1:2, time=0:4)

n = 1
time_to_remove <- unique(data$time)[-(1:2)]
unique_study <- unique(data$study)

for(i in time_to_remove) {
  studies_to_remove = sample(unique_study, size = n)
  time_to_remove = i
  unique_study <- setdiff(unique_study, studies_to_remove)
  data <- data %>%
    filter(
      !(   study %in% studies_to_remove &
            time %in% time_to_remove ))
}
data %>% as.data.frame()