Op-amp bias issue to to charging of DC blocking capacitor
Does there exist a neater solution to quickly bias up the circuit to 2.5V whilst not developing any DC voltage across the sensor?


There will always be a power-on pulse.

You can also replace C_DC with another opamp wired as an adder, which would add the required DC offset. However, it would need to be accurate, and since you mention the signal already has a DC offset on it, this would have to be known and compensated exactly, which is tricky.

In the end, shorting out the sensor might be the safest solution.

If the power-on pulse is a problem (you should measure it) then you could use a normally-closed relay or opto-MOS to short your sensor, and only open it when DC bias is fully stabilized.