From past discussions in the forum, I've gotten the impression that there do seem to be some key cultural differences. In German-speaking cultures, the onus seems to be much more on the person entering, particularly in places like stores and waiting rooms. But in English, in my experience, you don't need to greet total strangers at all unless you need to talk to them individually for some purpose.
In an office, it may depend on personality types. Extraverts and feeling types usually value greeting and being greeted; they're typically surprised that anyone else might not consider greetings important. For them, the question of who greets first is probably less important than that there's an exchange of greetings. But in general, yes, the person already there may well be the first to say good morning, because that person is in the host-like position of welcoming a later arrival. (Similarly, salespeople in English-speaking shops usually greet customers first, not the other way around.)
Introverts and thinking types, however, may experience greetings as mildly annoying interruptions. If an introvert has the misfortune to have a desk in an open office, it may be hard enough to get any work done without people walking by and chit-chatting all the time. (That may even be why the introvert has been there since 7 a.m. (-; ) 'Male techies' as in #12 do tend to be thinking types, but they're not the only ones, even though this type is often in the minority in the general public, especially in extraverted cultures like the US.
So perhaps part of English-speaking politeness is just to make eye contact before greeting. If someone looks up at you, then of course smile back, and if you want to, say good morning. But if someone is obviously busy and doesn't seem to want to look up, that may be a hint that it would be better to wait and say hi later, unless you actually need the person's help right then.