You don't seem to understand what a statistical model of observational data is, but I can maybe help a little. When building statistical models of observational data we attempt to explain the observed patterns of the data and attempt to attribute the variation in those data to causes; with observational studies we often use correlative analyses to draw inference about how the world works. Yes, correlation is not causation, but that just means we need to be careful with our inferences it does not mean we should not use or trust a correlative study. There is nothing causal about time in a time trend analysis anyway, time typically is included to represent some other environmental variable that covaries with time. In this realm of modeling, we can compare the fit of a statistical regression model where time is the independent variable and global temperature is the dependent variable other with a null model, or intercept only model, that has no correlative relationship. We could even do models with percent of green land cover, or better yet atmospheric carbon as the independent variables. The formal comparison of the statistical models can involve things like evaluating r-squared values, or, better yet, throw it all into an information theoretic approach to directly compare model fit for multiple models simultaneously. Again, This type of statistical modeling is retrospective and attempts to explain patterns in data. They type predictive modeling that you are referring to in this post is kind of a different class of modeling, theory building and testing; statistical modeling is a type of theory building and testing but as I said before, it is focused on explaining the past, not necessarily predicting the future. Predictions about the future can be derived from a good statistical modeling analysis, but given the stochastic nature of the systems we are discussing here, wide variability and uncertainty in future projects are expected. That is where risk assessment comes in and we as a society have to assess what are we willing to risk give the uncertainty in the model predictions.
However, the original discussion here was about a time series analysis that infamously cuts that data off at a specific year to tell an advantageous story to climate deniers. So just like I am no longer referring the 97% consensus at your suggestion, I suggest you drop the global temperatures haven't changed in 20 years line because it is just plain wrong.