By-Pass Capacitors for my SIM7600 Module
If your power supply contributes no current during the 577 us period then using: -

$$I = C\dfrac{dv}{dt}$$

and re-arranging to: -

$$C = I\cdot \dfrac{dt}{dv}$$

Gives you a value of \$C = 2 \times 0.000577 / 0.3\$ = 3850 uF

Assuming the power supply can provide an amp during this period means the capacitance can reduce to a little over 1600 uF.


  Should I be selecting capacitor having ripple current more than 2A?


You can use an electrolytic capacitor as the bulk energy provider and bypass it with (say) a 100 uF ceramic capacitor to handle the instantaneous requirements of the sudden load. This is best judged using a simulator for simplicity where you would use a bulk capacitor value of 3750 uF in series with its ESR and ESL all in parallel with a pure 100 uF capacitor. Micro-cap student version is free and so is LTSPice.

Your aim would be to make the ceramic capacitors value lower by experimenting with different ESR/ESL capacitors.