how was it possible for them to be able to wage war against so many large empires at the time and bring them to their knees?
u/mikedash gave you some great links. I also touched on this topic in Karatepe and Çineköy inscriptions: Luwian and Phoenician and Sea Peoples.
Your question is based on a highly questionable premise, however, and requires taking Egyptian inscriptions literally. Unfortunately, many Youtube videos and popular history books have a habit of doing this and assume a singular cause for destruction levels, with an accompanying map of the Mediterranean showing all of the sites supposedly destroyed by the Sea Peoples. It is very difficult to say how much of this destruction can actually be attributed to the Sea Peoples as opposed to other causes like various other migratory groups (e.g. the Aramaeans), invasions by traditional rivals and enemies (e.g. the Kaška in northern Anatolia), rebellions among local people against Egyptian control, or simply freak accidents akin to the Great Chicago Fire. There seems to have been a Canaanite revolt at Jaffa, for instance, and some sites (e.g. Ḫattuša) burned down only after they were abandoned.
Egyptian inscriptions were written to express the Egyptian world-view, not to record "what actually happened." For example, an inscription on the second pylon at Medinet Habu lists the city of Carchemish in Syria as destroyed by invaders, along with other Syrian cities such as Arwad. We know from textual and archaeological evidence from Carchemish, however, that Carchemish not only survived the end of the Bronze Age more or less intact but thrived after the collapse of the Hittite Empire, with an unbroken royal line descended from the Hittite Great Kings of the Late Bronze Age. Indeed, many aspects of Hittite culture survived in southern Anatolia and Syria for several centuries, including religious beliefs and practices, Luwian and the Anatolian hieroglyphic writing system, architectural and artistic styles, administrative titles, and so on. Similarly, the Canaanite (or, as they would be called by the Greeks, Phoenician) city-states of the northern Levantine coast like Byblos and Sidon seem to have survived the end of the Late Bronze Age mostly unscathed.
The Egyptians were no doubt perfectly well aware of this, but they were not concerned with creating a faithful list of conquests and ensuring an accurate list of destroyed cities for future historians. The impact of the list was what mattered. A king who had (allegedly) defeated a confederation of enemies so powerful that they had destroyed the majority of the ancient Near East was a very mighty king indeed!
To use a different example from Egypt, the Libyan battle reliefs from Taharqa's temple at Kawa in Sudan are direct copies of Old Kingdom battles scenes like those from the mortuary temple of Sahure at Abusir, created nearly 1800 years earlier. Even the names of the three defeated Libyans were recycled. This doesn't mean that Taharqa was trying to bamboozle people into thinking he had defeated Libyan forces when he hadn't; rather, the reliefs are simply a timeless expression of the king's role as protector of Egypt and his obligation to bring forth order from chaos.
As for the Sea Peoples in Egypt, the inscriptions are classic examples of the Egyptian fondness for compressing events that took place over years or even decades into a single climactic showdown for dramatic effect. Was there ever a huge battle between Ramesses III and a confederation of sea-faring groups? Highly doubtful. As Barbara Cifola put it in "Ramses III and the Sea Peoples: A Structural Analysis of the Medinet Habu Inscriptions,"
All this leads us to think that the encounter related in the text of year 8 is probably nothing but the narrative condensation of a continuous long-lasting process, consisting of small skirmishes and rebuffs of repeated attempts at assault and penetration, into a single great military event to serve a precise propagandistic purpose...
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