It is often the case that a country receives aid from other countries to establish state institutions. This is very frequently the case after a country has been significantly weakened by a war, for example. To answer your question, you could use the role of the German army in Afghanistan, for example. The war in Afghanistan had significantly destabilized the country. Having been under the influence of the Taliban for so long, there were no effective state institutions in place. Part of the work of the German army in Afghanistan was to help the country to establish a new and more effective police force. This was very important work, as it helped the country to move on from the time of crisis by building a more effective police force, which helped to bring a bit more stability into the area. You could use this as an example to show that international aid definitely helped in the establishment of an effective state institution here.
You might also want to mention international financial aid for building schools in poorer countries. This is another example of how international aid is helpful in terms of creating effective state institutions. By providing the financial means necessary to improve a country's education system, international aid massively contributes to the establishment of schooling as a state institution. This allows people from the area to receive an education, which in return will lead to a better-educated local population.
However, it is important to point out that mere financial aid alone might not be sufficient for a state institution to be efficient. You might need to explain that international aid will be a lot more effective if the countries, who wish to provide financial aid to another country, also get involved in the practicalities. For example, they should ensure that the money is used effectively and efficiently by sharing their expertise and by offering practical help with regard to setting up and running these institutions successfully. This could be done by ensuring the staff receive proper education and training, for example.