Some engines are capable of delivering 100% of torque the second (within a couple 100ms) of hitting the throttle. To name a couple:
1. The Mercedes M278 twin-turbo V8 makes 700NM of torque between 1,800 and 3,500RPM. In other words, 700NM of torque is available from little above idle.
2. BMW B58 single-scroll turbo i6 makes 500NM between 1,600 and 4,500RPM.
Other turbo charged engines, such as those in supercars, have different kind of turbos turned for a more linear torque and power curve to better replicate their N/A predecessors, such as the McLaren M838TE which makes 620NM between 5,500 and 6,500RPM.
Lots of different engines out there with all kinds of different characteristics and power/torque curves.