Ok, I got it. The timing resolution is affected by the signal-to-noise ratio over the rise-time of your signal. You find the full formula herer:

https://arxiv.org/abs/1405.4975

Your sine wave input signal has a slow rise time, and therefore limits the time resolution. I reproduced your measurement with a 20 MHz sine wave and got the same result:

If I increase the frequency to 100 MHz and increase the amplitude, I get a better resolution:

This is 5 ps which is better than 37 ps, but still not 2.5 ps. This can only be reached by sending single pulses to the evaluation board which have a rise time of > 300 mV / ns, which can be seen here:

It is important to understand the relation timing - resolution vs. rise time / noise as explained in the quoted paper. If you have tiny pulses from your detector, you never will be able to measure excellent timing. This is physics, and not related to the specific electronics you are using.

Best regards,
Stefan