I pass someone do I say hajimemashite or not

So I was wondering if I really say Hajimemashite (hello to someone when you're meet the first time) to someone when I pass them for the first time, cause we're just saying hello, and we're not REALLY meeting, I was wondering if I say konnichiwa, ohayo gozaimasu, or konbanwa depending on the time of day, or do I just say Hajimemashite ?

I don't understand your question. Can you divide it into shorter sentences?

Meanwhile, "hajimemashite" is used in the same way the English phrase "Nice to meet you." is used.

Passing someone as in walking past a stranger? Hajimemashite is more something you would say when you actually meet someone for the first time, it's not really appropriate for just acknowledging some stranger's presence as you would on a morning walk when you sometimes say "hello" or "good morning".

No.

"Hajimemashite" is a "It is nice to meet you (for the first time)" or "how do you do" the very first time, let's say when you "meet" in the sense of getting introduced to each other/introducing yourselves to each other.

In other words, "hajimemashite" is for when you expect to have a sustained (not necessarily deep, but long-term) relationship with that person. Certainly not for someone you don't expect to ever meet again.

Certainly not for someone you don't expect to ever meet again.

Yes, in other words "hajimemashite" means that it's actually "nice" to meet you.