While I'd love that to be true, economist's predictions don't have a good track record. Is there any good examples we can use to give evidence of thus massive claim?
It's not exactly hard to find anecdotal evidence. For example, Haitian households living in the US had a 2015 median income of $47,200. I don't know exactly how to translate this into per capita terms, but Haiti has a per capita GDP of something like $730. I'm sure that these groups of people are not perfectly comparable in every way, but it's certainly suggestive that people can make a better life for themselves here than in Haiti. How do you think you would fare in Haiti?
If you want a more rigorous extrapolation, which tries to account for confounding factors and isn't limited to one pair of countries... you are going to have to look at the research (of economists).
That seems a little shortsighted. Do you also think climatologists and meteorologists are charlatans because they can't predict hurricanes or blizzards more than weeks in advance?
You'll have to do better than that, because the majority of economic literature does not attempt to forecast movements, it attempts to model them and understand them. The "track record" you speak of is not actually the track record of economics, it's just a meme armchair economists like to repeat (generally without a non-snarky defense of their point).