Hi, perhaps something like this. I have created a pretend dataset, but next time provide a reproducible dataset.
library(tidyverse)
# pretend dataset ---------------------------------
df <- tibble(site_name = c("a", "b", "c"),
`2020-09-30` = c(0, 1, 0),
`2020-10-01` = c(1, 2, 0))
# pivot then only the ones less than 1 -------------
df %>%
pivot_longer(-site_name, names_to = "dates", values_to = "count") %>%
filter(count < 1)
# # A tibble: 3 x 3
# site_name dates count
# <chr> <chr> <dbl>
# 1 a 2020-09-30 0
# 2 c 2020-09-30 0
# 3 c 2020-10-01 0