The trading empire of the Dutch Republic would be impressive alone for it's achievements in trade and warfare, but it's astounding when you realize that by 1600, the Netherlands had 1.5m for population! Compare that to 18m of France, or 9m approx of Spain, or 5.6m by England.
I get that they were very sophisticated and had advanced commerce, production and politics. But still... 1.5 million? How is that enough manpower to arm enough soldiers on land to prevent invasions, and sailors to operate a huge fleet? And given the immense wealth and manpower of Spain and Portugal compared to that of the Dutch - what prevented them from just dropping in on Amsterdam and burn it so to keep them out of their business? Or maybe drop in on Calais and march on land if they didn't have enough naval power.
I'm writing a paper on the Dutch army around that time at this very moment.
I'll try to answer a couple of your questions. One thing to know is that the military strength of the Netherlands varied greatly in short periods of time. I'll mostly be focussing on the period around 1600, because that's the year you mentioned in your question.
First thing to know is that the 'manpower' of the Netherlands itself doesn't really translate well into actual figures for the Dutch army. A lot of the troops recruited for the army actually came from the Holy Roman Empire, England, Scotland, Switzerland, France, Sweden and even the Spanish Netherlands. If you can recruit from other populations, your own 'manpower' doesn't matter as much. It should be noted that this was the case for many armies during that time period.
Actually finding suitable troops was not that easy, but the Dutch army had a system where they gave contracts to third parties to make sure enough new soldiers werer recruited. As long as they found enough willing (and sometimes forced) people to join, it was only a matter of financing.
Armies also weren't that big at the time to begin with. Large battles with 100.000 soldiers on each side like the all-famous Waterloo weren't common (if they happened at all!). In the Dutch theatre of war, the Spanish fielded around 60.000 men at it's peak during their offensive in the years 1590-1609. The Dutch managed around 30.000 to 50.000 during that time. (In the year 1607 a temporary armistice was established which eventually led to the twelve years' truce in 1609-1621. During that time the States-General of the United Provinces drastically decreased the number of soldiers in the Dutch army to around the 30.000 figure).
A lot of these troops also weren't active in field armies, but were mostly garrisoned in cities and forts. As Dr. H.L. Zwitzer notes: 'the military power of the republic lay primarily in its fortresses*, the so called dead-defences, where in peacetime the regular troops of the States were garrisoned.' Open pitched battles were rare, but there was one in 1600! The exact year you mentioned. At the battle of Nieuwpoort, Prince Maurits of Orange commanded an army that was to take the town of Dunkirk in Flanders. Dunkirk was a safe haven for Spanish privateers that posed a real threat to Dutch shipping. Both sides fielded an army of around (only) 10.000 soldiers. While the Dutch army managed to win this battle, this was an anomaly. Most field battles were lost to the Spanish. Prince Maurits (The Stadholder) did modernize (one could even say revolutionize) the army a lot during this period, but the idea that the Dutch army was a modern fighting machine that could match every European superpower might be a bit too much. After all, after 1607 fighting stopped between the Dutch andSpanish for a while so determining the direct impact for this military revolution is a bit hard.
*The litteral translation would be fortresses and fortresses, as he uses the words 'vestigingen en forten' in Dutch. These are two seperate words denoting seperate kinds of fortresses, but they both translate as fortress in English.
As for the last part of your question, ‘Just dropping in on Amsterdam’ is easier said than done. You’d have to sail through the North-Sea, while evading potential fleets coming to intercept, and then find your way to Amsterdam going through the very shallow Waddenzee. And as said before, an attack by land has to deal with the many garrisoned towns and fortresses.
More can always be said, but it was never really a case of manpower.
Sources (that I had on hand): Olaf van Nimwegen, Deser landen crijchsvolck: Het Staatse leger en de militaire revoluties, 1588-1688 (Amsterdam 2006). Dr. H.L. Zwitzer, De Militie van den staat: Het leger van de Republiek der Verenigde Nederlanden ('s-Gravenhage 1991) Raa, e.a., Het Staatsche leger, 1568-1795. Dl. II: Van het vertrek van den graaf van Leicester tot het sluiten van het Twaalfjarig Bestand 1588-1609 (Breda 1913). Raa, e.a., Het Staatse Leger, 1568-1795. Dl. III: Van het sluiten van het Twaalfjarig Bestand tot den dood van Maurits, Prins van Oranje, Graaf van Nassau 1609-1625 (Breda 1915).