Specific word to replace "set somebody up for something [positive]"
Solution 1:
"Prime" or "dispose" could be used appropriately.
The definition of "prime" (HERE) that applies to this situation would be "prepare (someone) for a situation or task, typically by supplying them with relevant information." The "market conditions" prepare/groom companies for "continued progress..."
The sentence with "prime" would be either:
Past experience suggests that these kind of market conditions can prime companies for continued progress in the long term.
OR
Past experience suggests that these kind of market conditions can prime companies to continue progress(ing) in the long term.
Note: The "-ing" in the second example can be added/omitted.
The definition of "dispose" (HERE) that applies would be "to give a tendency to." The "market conditions" give a tendency to have "continued progress..."
The sentence with "dispose" would be either:
Past experience suggests that these kind of market conditions can dispose companies to continue progress(ing) in the long term.
OR
Past experience suggests that these kind of market conditions can dispose companies toward continued progress in the long term.
Note: The "-ing" in the first example can be added/omitted.
Solution 2:
"Position" would be my choice, as it's a common construction in the business world and would seem to be apt for this scenario (position companies for continue progress). In fact, the Merriam-Webster example definition is almost precisely the scenario in the question:
positioned the company in the global market
Solution 3:
The market conditions give the companies the tools they need, so they equip them:
[Merriam-Webster]
1 : to furnish for service or action by appropriate provisioning
// equip an army
Used in the example sentence:
Past experience suggests that these kind of market conditions can equip companies for continued progress in the long term.
Solution 4:
As the context is economic, you could use enable.
Example:
Past experience suggests that these kind of market conditions can enable companies to continue progress in the long term.
(You could also use stimulate, facilitate or instil. Or perhaps inculcate.)