CURLcode curl_easy_setopt(CURL *handle, CURLOPT_TIMEVALUE, long val);
On systems with 32 bit 'long' variables, this option cannot set dates beyond the year 2038. Consider CURLOPT_TIMEVALUE_LARGE(3) instead.
CURL *curl = curl_easy_init();
if(curl) {
  curl_easy_setopt(curl, CURLOPT_URL, "https://example.com");
  /* January 1, 2020 is 1577833200 */
  curl_easy_setopt(curl, CURLOPT_TIMEVALUE, 1577833200L);
  /* If-Modified-Since the above time stamp */
  curl_easy_setopt(curl, CURLOPT_TIMECONDITION, CURL_TIMECOND_IFMODSINCE);
  /* Perform the request */
  curl_easy_perform(curl);
}