Suggestions for accelerometer signal conditioning
simulate this circuit &ndash; Schematic created using CircuitLab

The zero G null adjust pot only has to correct source null error away from 1.65/3.3=50% so ratio of 1k/20K is 5% can be reduced to 2% for example.

Higher Gain is possible but choice of low input bias current, rail to rail type, unity gain stable Op Amp is necessary.

This is just one of many examples, not final version... after you specify full scale g and frequency limit.