The answer to this really depends on how the question is meant. The Articles of Confederation were the first actual constitution written for the United States. If the question refers only to a national government for the new country, then the statement can be seen as true.
However, you can also say that it is false depending on how you want to interpret the question and how you see certain events. For example, in 1754, Benjamin Franklin proposed the Albany Plan of Union. This was an attempt to create some form of a government that would have some degree of authority over all the colonies. Was this an "attempt at creating written law" on the part of an "American government?" It is hard to know given that the question is not as specific as it might be.
Overall, the Articles of Confederation were the first written constitution for the new country. In this sense, they can be seen as the first attempt by a truly "American government" at creating a constitution.