pivot_wider() requires a set of columns that uniquely identifies each observation. Your observations are not unique, so id_cols is defaulting to all columns.
You will need to create unique identified for each observation.
Since your screen shot of your desired outcome is not complete, hopefully this attempt will meet your goal.
df <- data.frame(ID = c(1, 1, 1, 2, 2, 2, 3, 3, 3),
Time = c(25,27, 26, 32, 23, 26, 25, 27, 19),
Identifier = c(rep('A22', 6), rep('B23', 3)),
Box = c(123,124,125, 123,124,125, 123,124,125))
library(tidyverse)
dfWide <- df %>%
unite(idTime, ID, Time, sep = '_', remove = F) %>%
pivot_wider(names_from = ID,
values_from = Identifier:Box)