I understand that before Clausewitz, someone who wanted to learn about military strategy would probably learn about the military campaigns of Caesar and Alexander the Great, as well as many others. But as far as I understand, there is not a central piece of Western literature comparable to Sun Tzu’s The Art of War before Clausewitz.
The premises here aren't entirely right. When it is said that 'Sun Tzu and Clausewitz are known as the fathers to Eastern and Western military strategy,' it may be worth clarifying that we mean contemporary military thought where these two thinkers are perceived to be of fundamental importance. Largely out of Orientalism (both imposed and internalised), we tend to ignore the fact that the existence of the Sunzi bingfa did not deter the production of huge amounts of military texts in later centuries, not all of which are fully consonant with Sun Tzu's prescriptions. At the same time, we tend to forget that neither Sun Tzu nor Clausewitz operated in vacuums of military thought; both had contemporaries and predecessors – albeit much more of the latter in Clausewitz's case. Because, simply put, 'the West' didn't sit around twiddling its thumbs for 2000 years waiting for a military theorist to appear.
Sun Tzu's text is only one of many from its own time. We don't know for sure when this particular text was written beyond the early-mid 5th century BC, but that only gives the Art of War a slight chronological lead over a whole host of texts from the early Warring States period, written between the mid-5th and late-4th centuries BC. Examples include Taigong's Six Secret Teachings (Liu tao), the Sima fa, the Wuzi, and the Wei Liaozi, while a possible descendant of Sun Tzu, Sun Bin, wrote his own Art of War in the fourth century. When, in the late 11th century AD, during the Northern Song Dynasty, the former four were compiled alongside Sun Tzu's Art of War and two later texts to form the Seven Military Classics, Sun Tzu's text was only the third entry of the seven, suggesting that the perception of his primacy is more recent than that.
Of course, in the 'Western' world at this time, there were texts on military theory and practice in production as well. While Xenophon did not write a general treatise on military techniques, his Hipparchikos (Cavalry Commander) can certainly be considered a manual for particular military circumstances; while fellow fourth-century writer Aeneias Taktikos was said to have written wrote a whole host of military treatises, though only one, on defensive siegecraft, survives. While it got a bit quieter during the Hellenistic period, the 1st century BC to 2nd century AD saw a bit of an explosion in specialist military texts, such as Onesandros' (Onasander) Strategikos, Ailianos Taktikos' Peri Strategikon Taxeon Hellenikon, and two Strategemata, a later and more comprehensive one in Greek by Polyainos, and an earlier and better-structured one in Latin by the Roman senator Frontinus, written as a supplement to a now-lost general treatise on warfare.
But if we're talking military authors who appear to exercise a Sun-Tzu-sized influence on Western military thought, then we really need look no further than a late fourth-century text, Vegetius' de re Militari. At least in the former Western Roman Empire, Vegetius came to exert a massive influence on military thinking and conduct until the early 19th century. To cite just two examples, Christine de Pizan, one of the great French polymaths of the late 14th/early 15th centuries, often quoted or paraphrased huge sections of Vegetius in her writings on military matters, such as in her treatise on siegecraft; while the influential 18th-century French theorist Turpin de Crissé's two-volume Essai sur l'art de la guerre (1754-7) cites Vegetius liberally, along with some input from Onesandros, Polybios and Livy.
The Eastern Roman Empire saw no dearth of texts being produced either. The late 6th century Strategikon, conventionally attributed to Emperor Maurice, draws heavily on Onesandros and Ailianos Taktikos, but with significant original material relating to warfare against nomadic horse archers which Onesandros and Ailianos had not needed to deal with. Leo VI (r. 886-912) commissioned or wrote another Taktika, derived from Ailianos, while the late 11th century saw the production of another Strategikon, attributed to Kekaumenos. This is by no means an exhaustive list of Byzantine military materials, but it should be patently clear that there was by no means stasis in military thought.
Meanwhile, Chinese military thought continued. The last of the Seven Military Classics, the Questions and Replies between Tang Taizong and Li Weigong, is of uncertain origin, and while traditionally attributed to the early 7th century could have been produced any time between Taizong's accession in 626 and the compilation of the Seven Military Classics in the late 11th century. Still, its existence reminds us that military thinking was no more static in China than elsewhere. Bear in mind, of course, that the Seven Military Classics were simply an epitomised compilation of texts perceived to be foundational in Chinese military thought. It is somewhat surprising – though for that same reason rather telling – that a text from no earlier than the 7th century AD should be grouped as a 'classic' alongside six others, the last of which dates no later than ~196 BC – simply put, not only were significant steps in military thinking being made, they were also being recognised.
For an example of such developments, David A. Graff cites the example of Li Jing, minister for war under Emperor Taizong of the Tang, who in 629 defeated an Eastern Göktürk army at the Battle of Tieshan (Iron Mountain) with an operational plan that discarded one of Sun Tzu's key maxims, opting to encircle the nomadic army rather than, as Sun Tzu prescribed, offering a path of escape. The specific elements of his plan also differ heavily from Sun Tzu, and in fact Graff points out that, aside from the encirclement, Li's plan largely conforms to the model presented in Maurice's Strategikon! Of course, the point here is not that Tang generals were reading Byzantine military texts, but rather that similar experiences against similar enemies could produce quite similar developments in military techniques. Li Jing himself wrote a bingfa (Art of War) which sadly only survives in fragmentary form, but sufficient to demonstrate, at least as presented by Graff, clear parallels in military thought between Byzantium and China at this time.
The thing here is that we have a tendency to assume that Chinese military thinking is wholly Sun Tzu-based and thus inherently static. But there are two obvious counters. Firstly, that, as shown, innovation in Chinese military thought was frequent and continuous. Secondly, given the dominance of Vegetius in Western Europe until the French Revolution, we could argue on exactly the same basis that 'The West' has been guilty of the same level of military stasis until relatively recently. Of course, as we know, military theory and practice did change over time in both contexts: Sun Tzu and Vegetius offered useful rhetorical tools even if their general frameworks were actually being twisted or discarded completely.
The emergence of Clausewitz as the Western theorist par excellence was not an instantaneous affair. Clausewitz was but one of many writers in the wake of the French Revolutionary and Napoleonic Wars who sought to grapple with the vast changes in warfare brought about by the emergence of ideologically-driven citizen armies across Europe. During the wars, Archduke Charles of Austria, who was commander-in-chief of the Austrian army in 1809 and inflicted Napoleon's first battlefield defeat at Aspern-Essling, made some of the first major attempts at this with the Grundsätze der Kriegskunst (Principles of the Art of War) in 1806 and the Grundsätze der Strategie erläutert durch die Darstellung des Feldzugs 1796 (Principles of Strategy Explained through the Example of the Campaign of 1796) in 1814. Clausewitz's great Francophone competitor, Antone-Henri Jomini, a staff officer under Napoleon, wrote a treatise on grand tactics in 1805, and his magnum opus, the Précis de l'Art de la Guerre (Summary of the Art of War), in fact postdated Clausewitz, being published in 1838, seven years after Clausewitz's death in 1831 (the complete but unedited On War was published by his wife and editor, Countess Maria von Brühl, in 1832.)
In the Anglophone world, Jomini rather than Clausewitz would prove to be the major influence for some years – under Dennis Hart Mahan, the military curriculum at West Point to which most commanders of the American Civil War were exposed was largely Jominian. In practical terms, only the Prussian army was Clausewitz-focussed for most of the 19th century thanks to disciples like Moltke the Elder, and the apparent primacy in the Anglophone world of Clausewitzian thinking is at most quite recent and even then not that universal. In the mid-20th century, the two major British theorists, J.F.C. Fuller and Basil Liddell-Hart, were divided on Clausewitz: Fuller gradually developed an appreciation for Clausewitz, while Liddell-Hart criticised the 'disciples' of Clausewitz without necessarily clearly distinguishing between where he found fault with Clausewitz versus those who 'misinterpreted' him – moreover, modern Clausewitz scholars like Christopher Bassford would contend that Liddell-Hart was very much a misinterpreter himself. One of the most prominent (if controversial) Anglophone military historians, John Keegan, was notoriously anti-Clausewitzian in insisting on war as the production of culture rather than the extension of politics.