I’m on a POTS line with an X100P card. I think it picks up immediately(first ring) but I’m not sure. I haven’t put any special configuration to delay pickup.
If Asterisk picks up after first ring, it may not have the chance to pick up caller ID. (In N. America, most POTS deliver caller ID between first and second ring.) Try ztmonitor to listen to the incoming ringing to hear the FSK chirp.