Even better question: how large, physically, is that 20pF? If the answer is more than a few cm, end to end, then it's not going to behave as a capacitor, but a transmission line stub of some sort!
Note that 1ns * 700nA = 700aC and 700aC / 20pF = 35uV. You're looking to amplify and differentiate a step of this magnitude. Even if you don't need much signal level (low mV?), you're asking for a tremendous amount of gain at high frequency to turn that into a pulse versus a step.
There is also a noise associated with capacitance, independent of system resistance, or bandwidth (they cancel out). For 20pF at room temperature, this is 28uV.
In general, you are asking for the impossible.
If the detector and amplifier are cryogenically cooled, it may still be possible, but you may find it is more productive to fix the detector.
Tim