Are those sentences with 'solution to' correct?

There are at least two explanations for the construct. Both depend on ellipsis. My suggestions for the omitted material are shown {so}.

One solution to {the question of} solving unemployment problems is help from governments.

One solution to {the} solving {of} unemployment problems is help from governments.

Ellipsis = a situation in which words are left out of a sentence but the sentence can still be understood

Cambridge

Are those sentences with 'solution to' correct?

Not from my perspective as a native speaker, no

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From your comment that you're trying to directly solve the problem the sentence mentions, I'd connect the use of "solution" directly to the use of "problem"..

• One solution to unemployment problems is help from governments.
• One solution to the problem of unemployment, is help from governments.

..or if you want to connect "solve" to the problem, drop the use of "solution"..

• One method of solving unemployment problems is help from governments.
• One way to solve unemployment problems is help from governments.

..rather than a sentence construct that causes the reading user to closely associate "solution" with "solve" - because solving is "providing a solution" it doesn't make sense to "solve a solution".

If you want to outline that the solution is one of many, add some more wording to distance "solution" from "solve", and more clearly create a "set of problems that are solved" so you can talk about one of the solutions:

• One solution, in the typical set of ways we solve unemployment problems, is help from governments [in the form of..]