Correction of False Claims in Question
In economics it is generally agreed that free trade benefits all participants.
This is simply not accurate, there is no scholar of international trade that would defend such proposition. Trade does not need to benefit everyone. One could perhaps defend position that trade benefits everyone in the long-run, however in short-run there are definitely at least few losers from free trade. You can see this in models presented in any advanced or even undergraduate textbook such as Feenstra Advanced International Trade: Theory and Evidence, or Krugman, Melitz & Obstfeld International Economics: Theory and Policy.
Let me give you trivial example, when country is closed to trade in some product that foreigners can produce more efficiently then local manufacturers benefit. This benefit is at the expense of wider public (i.e. consumers), but local manufacturers can earn profit exploiting the fact that consumers are not free to choose more efficient producer abroad. Eliminating trade barrier will hurt at least these local manufacturers as they will either have to put more effort and investment in improving their craft which is costly or go out of business.
Economists are in favor of free trade not because it would always benefit everyone (although sometimes it may), but because generally speaking, on net balance, benefits of trade to society can be shown to outweigh costs in wide range of possible scenarios (see the above cited books). As a consequence, there is always possibility for society to redistribute part of the benefit to the losers to compensate them for the loss (even though this does not always happen politically). Nonetheless, it makes society on net better off, which is not same as making everyone better off period.
Trade is also shown to have some dynamic effect on economic growth (see Feenstra Advanced International Trade 2nd ed pp 331-360). Hence, once could possibly defend the statement that in a long-run everyone is better off. In the end even losers from free trade will see their incomes increase thanks to economic growth, but that is not the same as blanketly state that everyone is always better off.
Next, in most of the cases where one can show protectionism is actually theoretically better, the result often critically depends on assuming that other countries do not retaliate and implement their own protectionist policies, which is often unrealistic. Finally, even in scenarios where it can be shown that some form of protectionism can be welfare improving the protectionist policy is simply too complex to be easily implemented by policy maker, and there is simply too much opportunity for policy makers to be captured by business interest (see Krugman 1987).
Answer
There is evidence that trade openness generally benefits developing countries.
For example, Raghutla (2020) shows that in a panel analysis of multiple emerging markets more open emerging markets grow faster. Tahir & Khan (2014) show in their studies of Asian countries that open Asian countries develop faster. A wide review of literature by Hye & Lau (2015) also argues there is positive link between openness and economic development.
A good overview of evidence is also provided in basic textbook mentioned previously. Krugman et al International Economics 9th ed pp 249-284 has an overview of discussion of free trade. It also supports the idea that generally speaking free trade/trade openness has on net benefits for developing countries. For developing countries specifically 286-298 is most relevant. An undergraduate textbook is actually a best place for a layman to start because undergraduate textbooks present the consensus positions rather than fringe ideas. Just skip all the introductory theoretical models that serve mainly didactic purpose for people who want to later become professional economists and go to discussion directly.
