Contributing to public German social security without a job

Although I know a lot about such subjects, this is beyond my level of knowledge. Social contributions; paying for health insurance if one is on  a public option plus retirement insurance and disability care is all based on earned income rather than unearned income from investments. Taxes on investments have different rates and are something separate from social security contributions. It is unusual for a non-retired person to come for a longer period of time and not work. As an EU citizen I am guessing it is possible but I am not sure. What is not allowed is that one gets benefits like unemployment in the first 2 years. The main thing is that they don’t want to have to pay for people but if they have enough investments then this should not be the problem. But one has to have health insurance and if they are neither working nor considered unemployed then which insurance do they need to get? I can only guess it would then be private insurance but only the experts can say for sure.

Thanks for your response, TominStuttgart.

I am definitely not interested in getting any unemployment benefit. The main (and only) reason for contributing to the German social security would be to preserve the pension rights for old age in my home country. As I said, all my taxes, which stem from capital gains, would be paid to the German administration.

I understood you weren’t looking to get unemployment; I only mentioned it in context of what especially concerns the government officials. But I don’t think there is a way to voluntarily contribute into the social system. How would it be determined what one should give? I think officials would refer you to cover things like health care and retirement through private insurance and investment possibilities. Maybe there are some exceptions I’m not aware of but one cannot expect them to change their system and protocol to accommodate a few people.  And again, of course one has to pay any tax liability due on investment income but this is not a social security contribution.

Apart from German health insurance, which is compulsory for any resident (and contributions will in your case be based on your world income and at double the rate a German employee pays at the same income - so don't expect it to be cheap!), I believe there is no way to contribute voluntarily and independently from salary earned in Germany to unemployment or pension insurance.
In addition, contributions paid in Germany do not easily (and often not at all) transfer to other countries' systems. So you may want to continue paying into your home country's system.
You can also join a private pension scheme, which are numerous and typically offer better returns than the public system.
But all this is so complicated (and so important) that I must suggest you get professional assistance! (The same can be said about the tax situation!)