Greetings! This is a rather interesting question, and perhaps one that students of the First World War take for granted when studying the origins (an infinitely nuanced and ever-evolving task I assure you) of the seminal tragedy of 1914-1918. I must ask however, what exactly OP means by "this question is based on hypotheticals". For the sake of providing my take on the question, I shall interpret "hypotheticals" as meaning that Austria-Hungary had something to gain from blaming Serbia for the assassination of Archduke Franz Ferdinand, and thus frame the response around Austria-Hungary's aims in blaming the Serbian government as responsible for the death of Franz Ferdinand in Sarajevo. Let's begin.

Note: For the sake of accuracy, I have decided to stick to the use of "Austria-Hungary" or "Austro-Hungarian Empire" rather than simply "Austria".

When the Archduke was shot by Serbian nationalist Gavrilo Princip on the 28th of June 1914, the Austro-Hungarian government quickly realised that the Serbian government was, in one way or another, a very likely supporter of the assassination plot. Of course, as is commonly known nowadays, Princip and his fellow Black Hand Gang members, or Ujedinjenje ili smrt members (Unification or Death - the proper name for the Black Hand Gang), were most likely acting on their own, without the knowledge of the Serbian government or their full endorsement. Note the "most likely" here, we may never know for certain who in the Serbian cabinet knew of the assassination attempt, and what role they played in ensuring that it was carried out successfully (I go into more depth on this troublesome question here). What we do know however, is that the Austrian government was rather quick to capitalise on the fact that a Serbian national had carried out the shooting of their Archduke.

Even before the funeral on the 3rd of July, and whilst the Empire was still mourning the death of their heir apparent, elements of the government and press began pushing for war. The "South Slav Problem", as it was known, had been a thorn in the side of the Austro-Hungarian Empire for decades, and now seemed like the perfect opportunity to crush Serbia; the nation most associated with such nationalistic (and anti-Hapsburg) sentiments. The Balkan Wars of 1912 and 1913 had already shown how slow Austria-Hungary was to react to uprising in the Balkans (which many politicians in the empire saw as "their region" of influence and control). Even by 1914, the Austro-Hungarian Empire seemed to be on the verge of collapse, owing to its multi-ethnic composition. George Macaulay Trevelyan, one of the great British historians of the era, remarked as such in a paper in 1915 (a heavily biased one mind you, but with good insight nonetheless):

"The Empire of Vienna and Buda-Pesth [sic] is an anachronism, dependent now upon Prussian arms. It is the domination of two races, the Austrian-Germans and the Magyars, over half a dozen other races...For the tyranny exercised over the Croatian South Slavs in Hungary has involved as a corollary [following condition] the repression of the Serbian South Slaves in Bosnia. And the repression in Bosnia has in turn necessitated a hostile attitude on the part of Austria-Hungary toward Serbia...it [has become] more than ever essential to the Austrians to prevent the further development of Serbia, after her victory over the Turks, lest she should become the liberator of the South Slavs."

In essence, by assassinating the Archduke to the empire, Princip was inviting the Austro-Hungarian government to justify a casus belli on Serbia, giving it the necessary reasoning (or so its warmongering politicians believed), to present the invasion of Serbia as a necessary move to prevent further revolt and violence in the empire's Balkan provinces. In doing so, Austria-Hungary would gain the means to end (or so it hoped) the nuisance that Serbia posed to her Balkan interests and Slavic populations.

On a slightly relevant tangent here - it is a tragedy that the man who Gavrilo Princip and five other members of the Black Hand Gang aimed to assassinate in Sarajevo on that sunny summer morning in June 1914 was perhaps the only man who could have mended the rift between Austria-Hungary and Serbia. Archduke Franz Ferdinand was a known proponent of the concept of a trialist empire, in which the Slavic populations of the Hapsburg dominions would be given equal representation in the assemblies of the empire, which the Austrian and Hungarian populaces already possessed. The newly integrated provinces of Bosnia and Herzegovinia were particular hotspots of the empire, and Ferdinand’s visit to Sarajevo was intended to be a show of goodwill on behalf of the throne in Vienna (alongside, as some have theorised, an effort to rally Slavic support for his trialist ideas). On the date of his assassination, some who held the strings of power in Vienna had clamouring for pre-emptive war with Serbia for years already. One among them was the Chief of the General Staff: Franz Conrad von Hötzendorf, but his prior calls for hostilities had been deemed too escalatory and not worth the effort.

When news of the assassination of the Archduke Franz Ferdinand and his wife Sophie in Sarajevo reached the Austro-Hungarian government, the general mood was immediately one of hardline action and anti-Serbian rhetoric. Hötzendorf was the chief proponent of striking at Serbia, but he was by no means the lone wolf in the Austro-Hungarian government who wished to neutralise this longstanding threat from the Balkans. There were however, three key problem with declaring war quickly. The first was simple and rather coincidental: the Austro-Hungarian army was on harvest leave. It was not due to end until the 25th of July, and calling back the troops for active deployment too quickly would not only leave the food supply in critical disarray, but upset the delicate mobilisation plans which Conrad and his staff had revised for years. Until the troops returned from the fields (the ones on the farms, not those of a battle), the Hapsburg armies would be unable to initiate hostilities against the Serbians.

Secondly, there was the Russian concern. Everyone in the Austro-Hungarian Foreign Office knew quite well (as in previous Balkan Wars), that a war against Serbia would no doubt propel the Russians to support their Slavic ally in southeastern Europe. Here we have the first sign of "awareness" that a "localised" conflict between Serbia and Austria-Hungary would likely lead to a greater conflict with the Russians. Third, and herein lies the critical point of the question, was the German factor. As in previous war scares, the Austrians were reluctant to take the initiative in declaring war unless they had the firm support of their Dual Alliance partner in Berlin. If German support was secured, then the politicians in Vienna would have added another domino which would fall upon the declaration of war with Serbia.

I shall not deal too much with the process and developments which led up to the "blank cheque" which the German Imperial Government issued shortly after the Austro-Hungarians dispatched an envoy to seek their support, but for more information on whether the Austro-Hungarian leadership (or the German leadership) was aware of the "ripple effect" of the declaration of war against Serbia, see this thread here. I shall instead conclude by returning to the question at hand:

"why was Serbia blamed for the assassination of Archduke Franz Ferdinand? What would Austria-Hungary have to gain from it"

Regardless of whether or not the Serbian government knew of Gavrilo Princip's motives before the fateful morning of June 28th, Austria-Hungary held them accountable for the actions of one of their citizens, seizing on an opportunity to rid themselves of the Serbian menace (if you will), that had hung like a phantom over their Balkan provinces and South Slav populations. The crushing of Serbia, it was argued by many within the empire, would put an end to the external threat posed by this neighbour of the Hapsburgs, who had long been a problem in its southern flank.

Hope this response helps, and feel free to ask any follow-ups as you see fit!