Falstads circuit simulator : capacitors have initial voltage?
This is not really an answer, but a possible workaround.

Falstad uses the URL to hold the circuit definition.

It contains the starting voltage of the capacitor.

This URL starts the capacitor at 1 mV.

https://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ac+-80+272+-80+160+0+0.00001+0.001%0Ap+48+160+48+272+1+0%0Aw+-80+272+48+272+0%0Aw+48+160+-80+160+0%0Ag+-80+272+-80+304+0%0Ao+1+64+0+4098+0.001220703125+0.1+0+1%0A


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This URL starts the capacitor at 0 V.

https://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ac+-80+272+-80+160+0+0.00001+0.0%0Ap+48+160+48+272+1+0%0Aw+-80+272+48+272+0%0Aw+48+160+-80+160+0%0Ag+-80+272+-80+304+0%0Ao+1+64+0+4098+0.001220703125+0.1+0+1%0A


This is how the URL breaks down.    

https://www.falstad.com/circuit/circuitjs.html

?cct=$

+1
+0.000005
+10.20027730826997
+50
+5
+43
%0A

c                   capacitor
+-80
+272
+-80
+160
+0
+0.00001
+0.001              starting voltage
%0A

p
+48
+160
+48
+272
+1
+0
%0A

w
+-80
+272
+48
+272
+0
%0A

w
+48
+160
+-80
+160
+0
%0A

g
+-80
+272
+-80
+304
+0
%0A

o
+1
+64
+0
+4098
+0.001220703125
+0.1
+0
+1
%0A


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addendum:

Searched through the source code at https://github.com/sharpie7/circuitjs1

Found this in CapacitorElm.java.

void reset() {
    super.reset();
    current = curcount = curSourceValue = 0;
    // put small charge on caps when reset to start oscillators
    voltdiff = 1e-3;
}