That catch-22 is supposed to be broken by the bank. It's a two phase commit where you open the account in a special state where you can only deposit the capital. Then the bank gives you evidence you've done so, you take that to the notary and open the company, then send the evidence you've done that back to the bank to convert it into a full account.
It's a bizarre system that Switzerland uses too. I've done it twice. Unfortunately the German speaking world has a lot of rules that are trying to eliminate all risk for investors and employees. The GmbH/AG capital requirements are just the start.
The next fun thing you might have encountered, at least in Switzerland, are rules that literally say your company's assets can't fall below 50% of your initial capitalization. If it does you're supposed to raise funds or make more investment of your own private capital and this rule pierces the usual liability requirements. Even more fun: it turns out that this law isn't actually enforced and locals regularly ignore it. But bad accountants won't tell you that. They'll just inform you of the law when you do your yearly accounts.
Then you have wealth taxes that cover the valuation of a startup as if it were a cash position. So if you raise $100M in investor funding then whatever shares you have left over are considered to be liquid assets you can offload at will, and are wealth taxed as such. The fact that the shares don't trade in a liquid market is irrelevant to the tax authorities. In Zürich at least that got patched by the local tax office deciding that startup shares aren't counted for the wealth tax, but this just means you have to be able to convince the tax authority that your company is a startup. The way they determine this is more or less just the opinion of whoever at the tax office assesses your case. Does it sound "startuppy" enough?
Fixing this stuff isn't hard, but it never gets fixed because European politics is both quite stagnant and dominated by people who view hostility to business as a virtue signal. They don't want to fix it because they think businesses are sort of like oil fields. They just exist, lying around naturally, and the only question is how to maximally exploit them.