There is no "most acceptable" form of greeting for e-mails. It depends on so many factors:
- whether you are writing to an individual (by name) or to a company or department;
- whether you know the person to whom you are writing and, if so, how well you know them;
- whether you are on first-name terms with the person;
- whether the message is for business, personal, or other private purposes;
- whether the message itself is formal or informal;
- possibly whether the message is likely to be forwarded to, and/or seen by, other people.
Personally, I avoid using the time of date in a greeting (or elsewhere in the message), except in certain circumstances, such as:
- it is relevant to the message;
- I know what timezone the recipient is in;
- possibly, whether I know how likely the recipient is to see the message fairly soon. (There is little point is writing "Good Morning" if they may not read the message until tomorrow afternoon!)
Furthermore, I question how many people actually read or notice the greeting and, even if they do, how many pay any attention to it.
In summary, my advice would be:
- if it is a formal or important e-mail, then write it as if it were an 'old fashioned' letter (see the answer from WS2);
- otherwise address it however seems appropriate to you.
Addendum in response to OP's comment: maybe I should ask what would be appropriate greeting when, for example, 'Guten Tag' in German or 'Dzień Dobry' in Polish is appropriate. They are not timezone-dependent.
I know 'Guten Tag' in German directly translated is Good Day, and will assume that the Polish is similar.
If it's a formal e-mail, the first of my summary bullet points still applies.
In some cases, such as e-mailing a support desk (as mentioned in the question), I may not bother with a preliminary greeting.
In some cases, using just the person's name (e.g. "John", "Mary", "Mr Smith") would be suitable, just as you may address them when speaking to them.
In other cases, I might use Hi or Hello. Personally, I regard those as fairly informal, but they seem to be accepted in semi-formal messages.
If you really want to use something close to "Guten Tag" that is independent of time, I would think that it would have to be Hello or Good Day. (But, at least in British English, when meeting someone, Good Day is used as Goodbye more often than as Hello.) Or you use a time-related greeting such as Good Morning, Good Evening, etc. based on when you write the message or when you think it is likely to be read.
[Beyond that, I'm inclined to say that this question is probably off-topic for this site, because any answers will be primarily opinion-based.]