I found there is a trend in time series data of rainfall using the ADF test. We made these data stationary by taking first difference. After this, the first observation is missing in rainfall data.
I'm not sure I understand your question. Are you trying to model time-to-time differences in rainfall as the variable of interest? If so, then yes, you necessarily lose the first year.
You might look into latent difference score models or autoregressive latent trajectory models for various ways to handle such data.