There are lots of techniques for making forward predictions- called projections- that look at investment curves and various inertial dynamics over circa 10 (at least) year timeframes.

Popularity itself is a fool's errand. Popularity is both manufactured and discovered, a stop motion virality. Some can create it but no one can predict it. The act of prediction changes the market.

And anyway, 2 years is basically tomorrow. It is not enough time for the capital investments occurring now to have material result. If you want to understand tomorrow you have to be looking back 10 years and tracing those investments through their maturation.

I’m actually not asking because of a desire to invest. Rather, for career trajectory.

In that sense, 2-3 years certainly isn't enough to become expert, but it is enough to make yourself desirable to companies when they start looking for people who can help them jump on the bandwagon.

Particularly if it’s a space you actually find interesting once you discover it.

Ok- so, in general, businesses don't hire low or mid level staff to jump on a bandwagon like crypto or AI. They hire leaders or expert consultants. This is a super frustrating trap that many many junior people fall into.

If you are junior, and you learn something specific in a domain, you can maybe be hired by a startup focusing on that specific thing. But that is tough to do without context. Many interesting/exciting technologies don't in fact have a useful business purpose. And "AI" or "crypto" are not specific enough, there are hundreds of potential specialities in each.

To get some context on specific technologies might develop business utility, try the Thoughtworks Tech Radar. Go through the trial and assess categories going a few years back, see what has matured into adopt and what is on hold. The Radar is specific. Each item is a specific tool, technology, or practice that an individual person can build expertise in.

With mathematical models. People suck at predicting the future of complex socially driven domains. The popular pundits are some of the worst predictors, but they do make easy media to sell.

Tetlock, P. E. (2017). Expert political judgment: How good is it? How can we know?-New edition. In Expert Political Judgment. Princeton University Press.

Politics is much harder.

The number of variables in tech to identify the most likely outcomes is actually quite limited.

Not sure, OP is asking about what is essentially a popularity contest. A popularity contest does sound pretty similar to a political race to me.