That's the point that your library's time_t reaches those values. But the point at which you will be 1.6Gs since the Unix v4 Epoch is in fact 27 seconds earlier, because your time_t hasn't counted the leap seconds over that period. To do that with Unix tools, you need to work with TAI timekeeping, not UTC, and remember that the (biased) zero point for TAI timekeeping is 10s before the Unix v4 Epoch.
% jot - 10 20 | while read -r d
do
printf "@40000000%08x%08x %s00Ms SI since the Unix v4 Epoch\n" \
"$d"00000010 0 "$d"
done |
TZ=right/UTC tai64nlocal
2001-09-09 01:46:18.000000000 1000Ms SI since the Unix v4 Epoch
2004-11-09 11:32:58.000000000 1100Ms SI since the Unix v4 Epoch
2008-01-10 21:19:37.000000000 1200Ms SI since the Unix v4 Epoch
2011-03-13 07:06:16.000000000 1300Ms SI since the Unix v4 Epoch
2014-05-13 16:52:55.000000000 1400Ms SI since the Unix v4 Epoch
2017-07-14 02:39:33.000000000 1500Ms SI since the Unix v4 Epoch
2020-09-13 12:26:13.000000000 1600Ms SI since the Unix v4 Epoch
2023-11-14 22:12:53.000000000 1700Ms SI since the Unix v4 Epoch
2027-01-15 07:59:33.000000000 1800Ms SI since the Unix v4 Epoch
2030-03-17 17:46:13.000000000 1900Ms SI since the Unix v4 Epoch
2033-05-18 03:32:53.000000000 2000Ms SI since the Unix v4 Epoch
%
Unix didn't adopt this Epoch and method of timekeeping until 4th Edition, somewhere in 1974 according to Unix historians. Yes, it's tricky to pin down the exact date of adoption. The Epoch was changed every year before then, as earlier versions of Unix measured time in 60ths of a second since the start of the year. This has made reconstructing Unix history from tape archives non-trivial. If you want to count seconds since the start of the first Unix Epoch, in 1st Edition, you have to count from the start of 1971. And no, that's not the same as how old Unix is.
(And yes, those values for 2023 onwards are somewhat speculative, as there will no doubt be more leap seconds.)