That's a pretty complex question with a lot to unpack. (Except: Minimize your contact surface vis-a-vis Germany. That part seems easy.)
First off: There is no such thing as a "remote friendly" jurisdiction. Estonia is trying to market this, but don't drink the Kool Aid. Someone is going to have to make a trip to the bank or the notary every now and then. They'll have to show their faces. They'll have to affix their signature to things. With ink on paper. You will have to deal with business partners who will think this way: "This guy is based where I am based. He knows that if he tries to defraud me, the police will come knocking. So he's probably not trying to defraud me, so it should be safe to do business with them." Versus "This guy is just someone on the other side of the planet sending e-mails. He knows that if he successfully defrauds me, I won't be able to do anything about it. Therefore I don't want to take the risk."
A lot depends on trust and interpersonal dynamics between founders.
If there is a lot of trust between the founders, I'd pick one of the jurisdictions where a founder is actually based. Say you pick the U.S. for ease of access to capital. This means that the person who is physically in the U.S. would probably end up having to liaise, frequently in person, with banks, accountants, government offices, etc. This puts a huge admin burden on that person, and also requires a lot of trust from the founders in the other jurisdictions that this person won't abuse their privileged position. If that founder drops out and there isn't yet any physical presences in the U.S. except for that founder, the others will be in a difficult position, because their own jurisdictions might not recognize that this is legitimately a U.S.-entity if there is no actual person in the U.S. who is connected with this entity. So that's why it requires a lot of trust.
An alternative might be: Set up 4 sole traderships and a "placeholder entity" in a zero tax jurisdiction that kicks into gear when real money starts getting to the table. So:
* Frank Deutschmann registers with German authorities as a German sole tradership.
* John Smith registers with U.S. authorities as a U.S. sole tradership.
* Aussie Australian registers in Australia as an Australian sole tradership.
* Sing Singapore registers in Singapore as a Singapore sole tradership.
* Startup Inc registers in Bermuda, with each of the four holding a 25% ownership stake.
Startup Inc passes the following resolution, and correspondingly makes a contract with each of the other four entities:
Revenues: We intend to sell an API to clients at $1 per 100 calls. To achieve that, Startup Inc will subcontract Deutschmann to run one server, Smith to run one server, Austrialian to run one server, Singapore to run one server. When a request hits a server, the server should use a random number generator: With a 25% probability it will handle the request itself. With a probability of 25% for each of the other three servers, respectively, it will redirect the client to one of the other three servers. Every partner has to pay the costs for their own server (AWS bills etc). Every partner gets to keep revenue of up to $100k per year for requests their server serves. Revenue in excess of that goes to Startup Inc. Intellectual Property: All IP belongs to Startup Inc.
The thing about the API was just an example, but you can think of analogous ways of e.g. splitting sales of widgets. The load balancing algorithm is obviously stupid, this was just for simplicity of exposition.
The great thing about this arrangement:
* As long as your api makes below $400k, Startup Inc doesn't handle any money. The German authorities only deal with a German sole tradership and tax it on its small profits, and don't care about the rest. The U.S. authorities only deal with a U.S. sole tradership and tax it on its small profits, etc.
* The Bermuda entity is the key to the whole thing and yet no jurisdiction would have a reason to scrutinize it or try to poke holes in it or attach any real significance to their respective citizens holding shares that are legally worthless in a company that is legally not really doing anything.
* No founder enjoys a privileged position that requires almost unlimited trust. If any founder drops out at this stage, the other three continue to operate almost as if nothing had happened.
* While it makes a lot of sense for the four to take advantage of economies of scale by sharing heavily, there is also potential for some autonomy which reduces the potential friction if there's something that founders can't agree on (e.g. every one goes to their favourite bank and hosting provider, picks an accountant they personally trust, etc.)
* If they end up making a loss, everybody gets a loss on their personal income tax which they can each offset against future earnings.
* In this stage the whole thing legally just looks like four people coordinating their efforts on a joint venture of sorts. But the main thing is each of the persons. Which is the actual reality of the thing at this stage.
* For each additional dollar that the API makes beyond the $400k per year, the whole thing starts gradually to look more and more like a corporation, both legally and in terms of the real life circumstance that the legal structure represents. Increasingly, what matters is no longer the four people, but the IP and money held by the Bermuda Inc with every individual being pretty replaceable. And the legal structure actually reflects that, automagically turning from joint venture-like to corporate-like.