To me there are some semantics involved here, I'd say you need to take a step back and think about a different adjoining question.
More than calibrate your parameters you need to estimate them since you have no points of reference for calibration i.e. no actively traded to Non-Linear / Vol products on this asset.
Calibration is simply trying to fit your model to market data by tweaking the parameters until you minimize some target function (like price difference) so that you're sure your model will match as closely as possible the observed market prices.... its a regression (using the term loosely) and your question is basically: how can I do a regression without a could of data points... you can't... but that doesn't mean you can't make educated/assumption driven guesses about your model parameters.
What I would do in this case, is I would look for proxy implied vols like:
- CLP RFR Historical Vols (per tenor ideally)
- USD RFR Swaption Rates
And try to put together an estimated one based on correlation assumptions.
Another way is I would ask myself If I had a swaption position today, what would be my risk limits and how much would it cost me to hedge it? simulate different paths of the relevant state variables and get an idea my PnL Vol, do this for each tenor, that would be your market data.
Finish it all off by estimating the model to the above values or a function of them and adjusting for any trades you might do by using the traded vols as new market data.
See this question too for some reference: Options when there's no VolSurf - Emerging/Frontier Markets
Hope this helps.