Learning TS itself takes minutes. Probably -seconds- if you're familiar with Java/C#.
The real learning curve is in the edge cases, of which there are plenty. Fighting with a 3rd party lib with incorrect type defs, dealing with cases common to JS that are hard to properly type (such as certain functional constructs), dealing with things missing from the TS compiler that are present in ES6/babel, etc.
Those things are quickly going away and may eventually be a non-ssue, but as of today, they're very real. That's in contract with languages that have the type system baked in from the get go, where it wouldn't be an issue.