No-insulation (NI) coil has been recognized as the most practical solution at present to achieve ultra-high magnetic field with the REBCO high temperature superconductor thanks to its passive quench protection mechanism which is originated from the inter-turn current bypass. However, for the NI technique, one of the most important obstacles to a more general application is the field delay which is also a consequence of the lack of inter-turn insulation. The proportional and integral (PI) active feedback control of power supply has been developed to achieve a designed field ramping rate. The efficiency of this method could however be affected by the measurement accuracy of measuring equipment, sampling frequency, control accuracy of power supply and other factors. In this manuscript, we tried to use a more fundamental method to mitigate the field delay. The point is, though unlike in insulated coils the field generated is not proportional to coil current in NI coils, they do have a certain linear relation for a certain coil. Based on the lumped circuit model, the current charging curve corresponding to a desired field excitation could be calculated for a NI coil. We verified this method on several solder impregnated no-insulation coils (SINoInCs) to excite their field with different rates, for which the field delay with normal charging method could be very large because of the very low inter-turn resistance. The test results show that this kind of fast excitation method could successfully achieve the desired field with high accuracy and mitigate the field delay from 130 s to almost 0 s. Besides, the large overshoot current introduced by the fast charging does not quench the coils even with an overshoot current which is almost double of the coils’ operating current.