If not some secret what size is that relay ? I dont see where is goal of it with relay coil sorry.
You should concentrate concept and question on inrush current of some device/load.
You need softstart.
Usually softstart is used for heavy load to eliminate high inrush currents of loads, such is transformators and other inductors. Just like Goldsmith mention.
Softstart you can make it for small money.
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If you need higher amperage use contactors, there is lots of contactors contact variants.
For sure 2 x 65A is not the job for some fresh relay from market ready to die.
;-)
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In post #5 you have similar thing from Synchopator.
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See triac softstart example, of course you will use adequate power triac and other parts for your design :
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You should know that triac dissipate power and relay/contactor not (if we dont count relay/contactor coil). And you will need appropriate heatsink for up to 40-60W of triac dissipation.