No, there is no trick.
But you need to distinguish between a private landlord and large companies. Those behave differently.
In the first case, that person might own from one or two apartments up to a few apartment buildings. Usually they would vet the applicants very closely and make a decision based on several factors.
- can you pay the rent (that one is obvious)
- how long are you planing to stay (because finding new tenants is a costly process)
- will you still be able to pay the rent later (also obvious)
- how will you affect the other tenants and the house
The last one can be broken down into a bunch of things. For example, if there are no children in the house yet, you wouldn't want to have a young couple where one or both is working. They might soon get a child, which is loud, and that would make everyone else unhappy. If you have to choose between a single man and a single woman, many landlords chose the woman because it they might think that a woman takes better care of the place.
A large company will essentially ask themselves the same questions, but they are easier to satisfy. Since you're a foreigner, you have a visa. That visa has a duration. If you can prove with your work contract and the type of visa you have that you're going to stay long and be allowed to stay long, that's usually fine. A company is used to those things, while a single, private citizen is not. So why would the private person bother if they can just rent to someone else?
What can help you in any case are the following things:
- If this is not your first apartment, get a Mietschuldenfreiheitsbescheinigung (long word, basically a letter saying that you were never late paying your rent) from your previous landlord(s); there are free templates on the web for that, and usually it's no problem to get the old landlord to sign it if you are really debt-free
- Get a Schufa score up front, even if they don't ask for it; usually that's a bit hard for newly arrived foreigners because there is no information about you
- Get a letter from your company saying that your contract is unlimited (if it is) and how you are important to them
- Have someone from your company help you search for apartments or make the initial contact through real estate sites like immobilienscout24.de with their company email and name
- Take a German with you when you go to check an apartment
Since the landlord always has a choice (until you sign a contract), they will go for the safe and easy option. And that's their right. So make them feel comfortable with you. For example, if it's an old lady that announced the vacancy in the newspaper, call and try to speak German, or have a friend call instead of writing an email, even if there is an address. In fact, always try German first, even if it's with Google translate help. Few people speak English in Germany. Germans have to do the same thing, they just have a head start because they speak the same language and might have more experience and are allowed to stay in Germany indefinitely.
Regarding the lack of responses, let me give you an anecdote. I am German, and I recently moved to Berlin from another city. I could not be in Berlin on working days when I was looking for apartments, so I wrote that down. Most places I contacted didn't respond. Some replied with texts like "the place is open for visitors on Tuesday from 3 to 4pm". So I wrote back or called, and said "can I have an appointment on the weekend, I live in a different city". The usual response, if there was one, went along the lines if "no" or "bad luck". It's business to them.
On one apartment in Berlin or Hamburg, there are probably from 100 to 200 people who want it. Half of them probably can't even pay the rent but they try anyway. Landlords need to filter, just like when you are looking for a job. So they filter on easy criteria.