You are really persistent in claiming that a MOSFET OP has no input current.
Technically, this is simply wrong. Any MOSFET has a certain leakage current, every technical IC is designed with protection diodes, etc. You'll refer to datasheest of real OPs to know the actual input current. It's at least some pA at usual ambient temperatures for general purpose OPs, down to fA for special "electrometer" OPs.
But assuming an ideal OP (and also ideal capacitor) with no input current doesn't solve the problem. It still leaves the voltage at the OP input node undetermined. You'll need a switch to charge the capacitor to a known voltage when starting circuit operation. If you have reason to presume zero charge of the capacitor (zero volts across it), you can simply replace the capacitor by a short, the other simple solution for your problem.
Either the series capacitor is part of a DC-blocking high-pass, then it needs a supplementing shunt resistor, or it's useless and can be omitted.