I think that I keep missing notifacations from other nations resulting in lowered prestige and no alliance, as I witnessed one box down there but wasn't quick enough to click it.
Ok about this "then you can blockade them, stealing cash, and occupy their turf with spread out troops." How do you blockade and steal cash? also wouldn't spread out forces be more easier for their ful stack to come around and annihalate each of your armies one by 1? Because so far whoever has the most numbers in their army seems to win a by a huge margin.
Here are some very basic tips:
This one I picked up from an AAR and never would have thought of by myself. At the beginning of the game, a huge amount of advisors are created. When advisors are created they are tied to a specific province (and therefore the country that controls the province). After one year, all the advisors that aren't hired by the various nations are dumped into the general pool. Exactly one year from the beginning of you game, if you pause the game, the advisor pool will be flooded with all those extra advisors, but it will only last one day because if you let another day elapse a bunch of the CPU nations will hire them. Basically, at the beginning of every game you should plan to pause the game exactly one year after the start of the game so that you can hire some excellent advisors (which can make a huge difference in the early game).
Another tip is to go into your options and change the message preferences. I have many set to pop up and pause (such as when someone declares war on me or my ally). You can also change many messages to act as pop ups instead of simply showing up as flags in the bottom right so you don't miss important messages. It may take a few minutes and you may want to tweak it a little more after you start playing, but in the end it is very much worth it and your settings will remain saved for future games. Once you get it where you want it, the message system because both intuitive and very useful. You get all the access you feel you need so that you aren't missing out on important things that could drastically change the fortunes of your country.
Another very helpful tip is to set your army and navy maintenance to fairly low levels in peace time. This was a huge eye opener for me when I first started playing since I wasn't used to having to deal with army and navy maintenance. Reducing maintenance simply reduces morale. If you are playing a Portugal game, for instance, you don't need to be paying full maintenance to the army and navy that is usually just sitting there doing nothing. Even when you are playing a nation that has a handful of potential enemies nearby you'll want to reduce maintenance fairly drastically in peace time. I tend to set my maintenance so that after I put maintenance at 100%, the morale bar will max out after two elapsed months. That is usually enough time to ward off any attack while also saving you a ton in peace time. With practice you'll figure out where this level lies (roughly).
In terms of your budget and how you allocate money, the best advice is to choose to focus on one thing at once. For instance, in a 1399 game as Portugal you could put all the treasury into the government slider because at level 4 you get to choose a national idea (after you get that, you could then choose trade because at level 4 you can build marketplaces). It is also important to not that you get a negative modifier if you are researching a tech ahead of it's time. You can see if that is the case by simply mousing over the bar for that tech in the budget screen.
Also, inflation is very important here. If you have the treasury slider set to be minting money, you will gain inflation. This is a concept many beginners simply don't fully grasp (including me when I started oh so many years ago). This can be quite harmful because it not only affects the cost of buildings, but also the cost of research for all the sliders. Even a small amount early can be quite costly over the course of several hundred years. Because of this, early in the game I often like to hire a master of mint so that I can mint a certain amount of money without accruing any inflation (it is great to get a 4-5 star master of mint at the pausing one year in because that allows you to mint quite a bit of money with no inflation hit). Having a guy like that can mean the difference between losing money every month (but ultimately making a profit at the end of the year with the census) and actually making money every month (on top of the census). In the early game when you need to build up your army, navy, and possibly build some buildings, the difference between -1 ducats a month and +1 ducats a month can alter your building plan by multiple game years.
Later on you can limit inflation with buildings, but early on having a master of mint can both help you avoid inflation while also allowing you to mint a small amount of money monthly so that you may actually be able to have a monthly income to go along with your yearly census. And just to emphasize, the census is what you live by in the early game. Even if you are losing a small amount of money per month (standard for much of the game), it is fine as long as your yearly census is giving you a decent income (and remember, this a game that lasts centuries so there is nothing wrong with spending two full years of national income on one new ship in the early game if that is what is needed).
One of the hardest adaptations I faced was accepting the fairly slow pace of the economy in the early game. One of the funnest things about the game is building up your nation over the course of 100-200 years so that money becomes less of a problem. Using the Portugal example, if you ally with Castille and build up a fairly small but decent army and navy and simply go along with their war requests (while not actually being an aggressor), you can have a very nice little isolated start. You can research government first and get your national idea. You could choose the one that allows you to colonize, or, the better choice, choose the one that gives you +10% trade efficiency (huge boost in the early game, especially when you have a center of trade (CoT) under your control). All you'd be doing at that point is keeping your CoT full of your merchants while possibly sending merchants to some of the other nearby CoTs. You can also maintain your relations with Castille so you don't lose them as your big brother. From there, you really just kind of research and wait until you get your next national idea (I think at gov tech 8) which will allow you to colonize. Once you get that you can colonize west Africa or you can try to explore into northwest Brazil. There are some good colonies in west Africa in terms of income and trade (slaves and ivory). If you get a base there you can rampage the African nations that are established and wipe them out and gain a nice little foothold that provides a good boost to your CoT (and thus your income since you should have 5 merchants there at all times).
One of the big techs is the trade tech that allows you to have a monopoly. The colonies you settle (or the uncivilized nations you take over) will trade into your main CoT. The CoT for Portugal at the beginning of the game generally goes from being the poorest in Europe to the richest. You can also establish new CoTs if the situation calls for it, which can bring in a ton of money by sucking in all kinds of trade goods from provinces that are in fairly unsettled land (North, South America and Africa).
This ended up being quite a long post, but I hope it sparked some interest. EU3 can be quite a blast when you have figured out the game mechanics. I think some of these basic tips can help to set a solid base from which to grow a nation (Portugal or otherwise). It is actually absurdly satisfying to do various things, like wipe out the Aztecs and take over their excellent gold income or send some decent gunpowder era troops with cavalry and cannons into India or China.
My favorite game was probably starting as Tuscany (2 province minor) when I unified the Italian peninsula and became Italy about 120 years into the game. From there I did some colonization, but my main goal was to take over India and China to dominate the trade goods from that area (spices and chinaware). I also had a nice little colony of about 12 provinces that started in the NE corner of Brazil and went down to the Sau Paulo area (basically a bunch of nice coastal provinces with excellent trade goods like coffee).