There are lots of different narratives that explain the war in the historiography of this conflict. Nationalistic discourses are the most common. For example, it is common to read that the war was a heroic defense of the patria or an irrational folly of a megalomaniac dictator. I am going to answer your questions by explaining the war through the lens of nation-state formation in the Río de la Plata. I think that this interpretation of the conflict is the most convincing and more holistically contextualizes the actions of the war within the larger regional trends occurring at the time.

The war turned out to be a one-sided affair, and if we think about the conflict from a modern perspective, imagining the juggernauts Brazil and Argentina (plus Uruguay) versus tiny Paraguay, the war really seems strange. As you mention, Paraguay had an estimated population of around 500,000 compared to the 12 million of Argentina and Brazil. Though there are historians who talk glowingly of the industrialization of Paraguay, in reality, this industry was modest at best. They had an iron foundry, but the economy might be better described as self-sufficient rather than industrializing. Internally, most Paraguayans were poor indigenous farmers who had no need for industrialized goods made in Paraguay or abroad. The Paraguayan military was well trained but small. They only had a small stockpile of modern weapons, and these were only marginally better than those Brazil had.

However, the geopolitical situation in the Río de la Plata in the mid-1800s was very new. Though there is a clear power disparity between the Allies and Paraguay, especially by 1865, these would not have been nearly as pronounced at the outset of the conflict and certainly not in the 1850s. Brazil had been struggling with rebellions in the 1850s, making it seem unlikely that they could maintain a protracted war on the southern frontier. Since independence, Argentina had never been a unified nation at all. The interior provinces did not recognize porteño hegemony and acted in virtual independence until the 1850s. Paraguay maintained close relations with Corrientes and the Littoral Provinces, disenchanted areas under the dominion of Buenos Aires that were seeing significant economic growth despite the civil wars. Paraguay even sent troops across the river into Corrientes when the province rebelled in the 1850s. Meanwhile, Buenos Aires considered Paraguay one of many renegade Argentine provinces; they did not recognize it as a separate country until the 1840s (and deep suspicion remained that Argentina would try to seize some or all of Paraguay in the future). Additionally, throughout the first half of the nineteenth century, the Argentine Confederation and Brazil remained rivals. They fought wars over the Banda Oriental, which would eventually lead to the creation of Uruguay. Following its creation, Uruguay also had been at war with itself.

In this chaotic environment, Paraguay was one of many sovereign areas whose power was comparable to other sovereign provinces in the Río de la Plata. They had successfully resisted integration for decades against Spain, Portugal, Buenos Aires, and Brazil, all while economic stability and national identity developed. However, by the late 1850s, Brazil and Argentina had begun coalescing into nation-states. Both consolidated control over their territories, developed burgeoning national institutions, and began looking abroad to settle existing border disputes. At this time, their interests aligned briefly in Uruguay, where both nations supported the Colorado party, rivals with the Paraguayan allied Blancos.

Yet this new order was not guaranteed to hold. In the event of war, López thought that the alliance between Brazil and Argentina would not hold (and it didn't; it collapsed shortly after the war). He expected to receive support from Corrientes (which did not happen because their invasion failed). He also probably thought that the newly consolidated Argentina would break out into civil war (which he was also correct about; Argentina lost more troops suppressing uprisings in the interior than they did in Paraguay, and conscription of gauchos was horribly unpopular with lots of gauchos taking off into the vast open spaces of the Pampas and the foothills of the Andes). But even when his predictions took place, they were not extreme enough to destabilize the new balance of power.

At the outset of the war, the Paraguayan army did win a number of victories when they invaded southern Brazil. Though Paraguay´s military was well trained, it suffered significant losses in Argentina and was further ravaged by outbreaks of disease. Paraguay also lost access to the outside world when the Brazilian navy cut river traffic, making it virtually impossible to get desperately needed military and humanitarian aid from abroad. The Allies never suffered this debilitation and were able to get more weapons from European suppliers. The sheer number of soldiers fielded by Brazil negated the advantages that Paraguay had on paper.

López might have been able to find an international power to mediate peace. The United States made a two attempts toward the end of the war. However, as it became clear to Brazil that complete military victory was possible, they were less and less interested in seeking diplomatic peace. Furthermore, the Allies signed a treaty in which they agreed to not end the war until López was removed from power. López obviously would never have accepted this provision, and the people generally felt like Brazil intended to wipe Paraguay off the map. So the war became a struggle to the last Paraguayan.

So I think I answered your questions in a very roundabout way. Although the outcome of the war was clear once Humaitá fell, it was not predetermined, perhaps even less clear to someone like López who was raised to see regional power dynamics that no longer existed.