Greetings! It is interesting why most websites say that Germany was the first country to declare when, as OP has already pointed out, Austria-Hungary was technically the first to declare war on Serbia on July 28th, 1914. The reason for this error in publication is mostly due to a western bias to an extent, and also a fairly reductionist view of the First World War. Note that this is a fairly short response due to the nature of the question posed, and touches more on the development/biases in the historiography of the First World War rather than an actual rundown of events in July 1914.

Though academic literature in the west now acknowledges the fact that Austria-Hungary was the first to declare war, for a fair bit of the previous 50 years or so, common textbook teachings in America and Europe portrayed Germany as the chief architect of war (especially after Fritz Fischer and other German historians introduced this idea in the the 1960s). Unfortunately this response cannot say for certain at what point website content creators (or even those textbooks) took that "chief architect" line and turned it to mean "first to declare war". In any case, such a statement is generally wrong, as the German "blank cheque" (which may be what the websites are referring to), was not actually an open declaration of war against any nation. In diplomatic terms, Austria-Hungary was the first to open armed hostilities in 1914.

Would OP mind linking these websites in question, and perhaps I might then be able to provide some context/explanation or a simple "that's rather wrong" for why Germany is mentioned as the first nation to declare war in 1914.