So do I! Simply divide the 3kW expressed as watts, i.e. 3000w, by 12v, gives 250A, ignoring losses. Actually, seeing that at that load the battery will be lucky to produce more than 10v, make that 300A, if the inverter efficiency is 95% at full load (being generous), around 315A.
I would be worrying about your battery rather than the Anderson plug!
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