I am not sure I understand the question completely but I believe it is one of the options below.
library(gapminder)
library(tidyverse)
# Create initial year for all countries
gapminder %>%
group_by(country) %>%
mutate(init_year = year[1])
#> # A tibble: 1,704 x 7
#> # Groups: country [142]
#> country continent year lifeExp pop gdpPercap init_year
#> <fct> <fct> <int> <dbl> <int> <dbl> <int>
#> 1 Afghanistan Asia 1952 28.8 8425333 779. 1952
#> 2 Afghanistan Asia 1957 30.3 9240934 821. 1952
#> 3 Afghanistan Asia 1962 32.0 10267083 853. 1952
#> 4 Afghanistan Asia 1967 34.0 11537966 836. 1952
#> 5 Afghanistan Asia 1972 36.1 13079460 740. 1952
#> 6 Afghanistan Asia 1977 38.4 14880372 786. 1952
#> 7 Afghanistan Asia 1982 39.9 12881816 978. 1952
#> 8 Afghanistan Asia 1987 40.8 13867957 852. 1952
#> 9 Afghanistan Asia 1992 41.7 16317921 649. 1952
#> 10 Afghanistan Asia 1997 41.8 22227415 635. 1952
#> # ... with 1,694 more rows
# Filter the observation when the year is equal to initial year (e.g. 1952)
gapminder %>%
filter(year == "1952")
#> # A tibble: 142 x 6
#> country continent year lifeExp pop gdpPercap
#> <fct> <fct> <int> <dbl> <int> <dbl>
#> 1 Afghanistan Asia 1952 28.8 8425333 779.
#> 2 Albania Europe 1952 55.2 1282697 1601.
#> 3 Algeria Africa 1952 43.1 9279525 2449.
#> 4 Angola Africa 1952 30.0 4232095 3521.
#> 5 Argentina Americas 1952 62.5 17876956 5911.
#> 6 Australia Oceania 1952 69.1 8691212 10040.
#> 7 Austria Europe 1952 66.8 6927772 6137.
#> 8 Bahrain Asia 1952 50.9 120447 9867.
#> 9 Bangladesh Asia 1952 37.5 46886859 684.
#> 10 Belgium Europe 1952 68 8730405 8343.
#> # ... with 132 more rows
If you have date and you want just the year you can use :
lubridate::year("2000-01-01")
#> [1] 2000