I don't think there is any one rule that fits every case here. The golden rule, if anything, would be to not overburden the reader, but keep in mind what they can be expected to know up front. Not overburdening the reader includes not giving irrelevant facts just because you can; if the reader simply doesn't need to know what the expansion of the abbreviation is in order to fully understand the text, then consider whether you really need to spell it out in the first place. Maybe a footnote would be sufficient, and you don't need to include it in the prose?
You do say "technical" writing, so I'm going to go with some technical terms. Would you rather use...
radar which is accepted as a word these days, while originally it was an abbreviation for either radio detection and ranging or radio direction and ranging.
PC or personal computer?
SMS or short message service? This one becomes more complicated because when most people use the term "SMS", they aren't really referring to the infrastructure but rather to the text that they are sending to a recipient cell phone.
IPv6, which is a widely accepted term, or Internet Protocol version 6?
LCD or liquid crystal display?
TV or television receiver?
car or automobile? (Particularly in languages where the word for car more obviously derives from the word for automobile, such as in Swedish where car is bil and automobile is automobil.)
I think you see where I'm going with this. At some point, you simply have to assume that the reader is familiar with some of the context in which your work exists. Otherwise, we wouldn't even have anything that qualifies as a meaningful language.
For your example of NATO the North Atlantic Treaty Organization, also keep in mind the intended audience. If you are writing in a context where precision is critical, then obviously you should be using the full, official name. If your audience can be expected to know what NATO is, then you might consider just using the abbreviation, which is relatively widely understood in the western world. If your target audience can be expected to not have a clue what NATO is, then the chances that they will be able to understand what the North Atlantic Treaty Organization is probably aren't much better, so you will need to offer a short introduction anyway, at which point you can give the variant they are more likely to be familiar with first, and the other afterwards. For example,
NATO, the North Atlantic Treaty Organization or in French Organisation du Traité de l'Atlantique Nord, is a military alliance originally founded in 1949. As of 2017, it consists of 29 member countries.
With the introduction out of the way, you should be able to relatively safely refer to them by merely the abbreviation, NATO, later in the text.
If you are uncertain, I tend to find that a good rule of thumb is to use whatever Wikipedia uses for the main article on a subject. You'd probably rather use car than automobile, and sure enough, if you plug automobile into Wikipedia, you end up at the page named car.