Learn Dutch: Dat is sowieso onvermijdelijk. - That is inevitable anyway.

Yes! You could say Dat is nou eenmaal onvermijdelijk ("That is simply inevitable, and we just have to accept it"). However, sowieso changes the flavor slightly. While nou eenmaal focuses on resignation to an unchangeable fact, sowieso means "anyway" or "in any case". This sentence means that regardless of whatever else was just discussed, the outcome cannot be avoided.

How is the long word onvermijdelijk formed?

It translates perfectly to "unavoidable". The prefix on- means "un-", and the suffix -elijk acts like the English "-able". The core is the verb vermijden (to avoid). Recognizing these building blocks makes long Dutch vocabulary much easier to digest at this level.

Is sowieso originally a Dutch word? I recognize it from German.

You are right to recognize it—it is a direct loanword from German. However, it is fully integrated into everyday Dutch. You will hear Dutch speakers use sowieso constantly in informal speech to mean "anyway," "in any case," or "definitely."

What are some good native Dutch alternatives for sowieso in this sentence?

If you want to mix up your vocabulary, you could easily swap it with in ieder geval (in any case) or hoe dan ook (anyway / no matter what). Both are extremely common and carry that same sense of certainty regardless of the circumstances.