Pause till layer marker

Paste this on the Time Remap property (you’ll have to turn on time remapping first; cmd-opt-t). Now the nested comp won’t start playing till it hits a layer marker (asterisk on the numeric keypad).

try {
    m = thisLayer.marker.nearestKey(time);
    linear(time, m.time, outPoint, 0, outPoint - m.time);
} catch(e) {
    value
}