A travel health insurance policy or the European Health Insurance Card of another member state is NOT sufficient proof of adequate health insurance cover.
In the case of gainful employment, insurance cover must be guaranteed at the start of the employment contract. In this case, proof can be provided, for example, by a letter from the (statutory or private) health insurance company stating that you will be accepted - unconditionally - into the health insurance scheme from the date of entry.
In the case of family reunification, proof can be provided by submitting a letter from the (private or statutory) health insurance company stating that you will be accepted - unconditionally - into the family insurance scheme upon entering Germany.
In principle, all national visa applicants are free to provide proof of unconditional enrolment in a private or statutory health insurance scheme in Germany from the date of entry. If this is not possible, you can present an Incoming insurance policy.
You are welcome to submit a so-called INCOMING insurance policy at the end of the visa procedure, which, unlike regular travel health insurance, may not contain any cancelling conditions for a long-term stay.
The Embassy is not entitled to advice on a specific insurer or company. However, you could quite simply search the internet with the wording ’Incoming Health insurance for permanent stay in Germany’ and surely receive some options. Known companies are e.g. MAWISTA; Fintiba, Dr. Walter, ADAC, provisit, Care-Concept etc.