How to obtain the steady state response of the sampled periodic signal data?
The filter starts from a steady state of having no input when it is created.
The sudden start of signal is seen as a step to your filter, so it takes time to settle. As the filter is 1st order, it resembles RC filter so it's time constant Tau determines that it will have settled to 98% after time of 5*Tau. Besides it looks like the sampled signal does not start from zero either, but with a negative value.

When working in time domain, you must just wait for transients to settle and then look at the response. To speed that up, you might want to take a look at the filter state when it has settled, and initialize the filter state with that.