Freelancer in India from USA company and living in German

This is the Germany forum, so we cannot advise on the tax situation in India - you may want to ask a tax consultant there, and check if there is a bilateral tax treaty.

I assume, in the following, that you hold a German visa that allows freelance work (otherwise you have bigger problems!) and that you have properly registed as freelancer or own a business for this.

You are definitely tax-liable in Germany, with your world income, as soon as you become resident. If there is a bilateral tax treaty (with India, or with USA? - three county arrangements are even more complex, so you should definitely ask a professional tax adviser about this!), it typically reduces the chance of being double-taxed, but usually gives taxation rights to the country where the work is perfomed (i.e, in your case, Germany).

In ANY case, you HAVE TO declare your entire world income in your yearly German tax declaration - because on one hand the tax authority (and not you) decides what is taxable here and what not, and on the other hand, even if it is not taxed, your world income will be used to calculate the progressive tax rate to be applied on the taxable portion (i.e. whatever you, and possible your spouse, earn in Germany). It will also be used to determine your German health insurance status and fees.

Since the issue is so complex (and doing it wrong, even unintentionally, is a criminal offense that can get you into deep trouble), you are well advised to engage a good tax consultant with experience in such international matters. They are rare!