Find a model with transfer function and real data

I am currently trying to create a model using a transfer function and my data. Here is my schematic:

Here is my transfer function:

My input signal is 2.5V for 10s, after which I decrease the voltage to 2.25V, and the charge amplifier rises to 2.75V.

Is it possible to create a model from this information?

I want to obtain my time constant, τ = RF * CF.

My initial approach was to take the natural logarithm of the measured values after the step, and then use the slope of the linear equation to obtain τ.

Here is the image for reference:

I have several charge amplifiers for which I want to determine the time constant. The decrease in the signal during the first 10s is due to the reference for the common mode, meaning each charge amplifier has a different common mode value.

I do not want to wait until my system reaches the actual common mode value to then make a step. Therefore, I want to calculate my time constant independently of the common mode value.

EDIT: Changed the tf to what @Franc said in the comments.EDIT2: To clarify: The Vcm input into the non-inverting input is stable, but not offset of the Vout of the Opamp.There is a 'stable' Vcm, but I will never or almost never reach it because my time constant (tau) equals RfCf, theoretically 100s for 37%, and for 5tau it's 99.3%. After resetting my system, it aims to reach the Vcm with a time constant of my RfCf, so after 500s, I will reach 99.3% of my Vcm. Therefore, I want to calculate my 'real' tau without considering Vcm.