It would be wrong to think that the Congress just established the Kingdom of the Netherlands all by itself. It mostly confirmed the Kingdom. Before the French rule, the house of Orange was in the Dutch Republic already influential enough to secure for itself succession rights to the stadtholder position. Late 18th century was a particular challenging time for them due to rising anti-Orange sentiments in the Dutch Republic and a stubborn stadtholder. The revolutionary times resulted in a revolt initiated by the Paris revolutionary regime and supported by the already troublesome Dutch Patriots that forced the stadtholder and prince of orange, William V of Orange-Nassau, to flee to Great Britain. It also resulted in the Batavian Republic which in reality was a French vasal state. This republic ended with the establishment of the Kingdom of Holland and Napoleon placing his own brother on the throne who de facto can be considered the the first king. After that the Kingdom was even fully annexed by France for a few years.

Regardless, French losses made the French rulers flee and a temporary triumvate was established in 1813 to quickly restore order. This triumvate, consisting out of 3 prominent Dutch politicians, did so in name [guess] of William Frederic (the son of William V), Prince of Orange-Nassau. Out of fear of anarchy and chaos they decided to establish a monarchy (and also because it was long holding wish by Orangists) and invited William Frederic (who was actually almost forgotten) to return. He accepted under condition of the establishment of a constitution and luckily for him the anti-orange sentiment had for a large part died down. William Frederic, crowned as William I, also secured the re-union with modern-day Belgium which became separated after the independence war of 1568-1648 and was subsequently always ruled by foreign powers.

The Congress of Vienna obviously needed to confirm this transition of power but did so. Partially because they needed stability and the house of Orange-Nassau, who supported the allied cause from the start and were strategically placed in Great Brittain, were seen as a rational choice. The union of Belgium (actually mostly called the Southern Netherlands or simply Netherlands at that time) and the Netherlands (to distinguish often called simply 'Holland' explaning why even today The Netherlands seems to have two names) was also confirmed because the allies wanted to have a strong buffer state north of France. And so it happened and it explains why there was no serious Dutch outcry against the monarchy (in the Southern Netherlands there eventually was, not so much against a monarchy since they were more used to centralized power anyways, but the 'Northern' rule due to growing frustrations and differences over time but that is a different story I think).