CURLcode curl_easy_getinfo(CURL *handle, CURLINFO_PRETRANSFER_TIME, double *timep);
DESCRIPTIONPass a pointer to a double to receive the time, in seconds, it took from the start until the file transfer is just about to begin. This includes all pre-transfer commands and negotiations that are specific to the particular protocol(s) involved. It does not involve the sending of the protocol- specific request that triggers a transfer.
See also the TIMES overview in the curl_easy_getinfo(3) man page.