Rough numbers: Assuming best quality, minimum series resistance values.
Battery resistance = 3 milliohms (likely higher unless a large AH capacity battery array)
BMS series MOSFET = 1.0 milliohm (better then cheap BMS)
Power cables = 1.7 milliohm (10 foot length pair of #2/0 wire)
Breaker = 0.5 milliohms
500 amp shunt = 0.1 milliohm
Misc inverter chokes, series lines, & terminals = 1 milliohm
Inverter capacitor ESR = 10 milliohm (highest quality, four 3,300 ufd, 40 milliohm ESR, in parallel)
Total series resistance = 17.3 milliohms (dominated by capacitors' ESR)
58.4 vdc applied voltage (16 x 3.65v cells)
Initial (t=0) instaneous surge current = 58.4 v / 17.3 milliohms = 3,400 amps
Time until surge current drops below 250 amps = 0.55 milliseconds
Time until surge current drops below 100 amps = 0.75 milliseconds
Time until surge current drops below 10 amps = 1.2 milliseconds
Time until surge current drops below 1 amp = 1.7 milliseconds.
Time until surge current drops below 0.1 amp = 2.1 milliseconds
The peak current may amaze you, this is probably worse case, but your system will still be quite high. Keep in mind the time is very short, only fraction of a millisec.
I did not include battery cable inductance which will be about 2 micro-Henries for this example (assuming they are taped together). That will cut peak current down a bit.
An average breaker contact can take 20 to 50 millisec to totally settle out open or close contacts so they have a lot of contact 'grinding' time.
Bottomline, do not use your breaker to turn on power.