What adverb (that isn't a participle) means for eternal? This adverb would only relate to eternal in time, and not necessarily infinitely in other ways. For example, "infinitely" means infinity in the quantity of intensity. The question is only about infinity in the quantity of time.
Everything below is extra information.
Eternally does not work because although it is based on eternal, it really means eternal from this point in time (aka, forever). Eternal means forever without a beginning, and forever without an end (existing forever in both the past, present, and future). It is understandable why this exists. When one says, "I am eternally grateful for you," It would normally be weird for someone to be eternally grateful of someone before a particular event.
The usage of "eternally" with the forever meaning is much more frequent then its usage as eternal. However words' definitions are in their usage. The word "nice" formally meant silly, but I would suspect that you would side with the new definition of friendly. If it can be proven that "eternally" with the definition of eternal, is just as frequent as "eternally" with the definition of forever. Then eternally would be an answer.
Always doesn't work because always' means "on every occasion" (According to its top definition). Eternal doesn't care wheter it is time for an occasion or not. "In an eternal manor, I run late," literally means without any form of interruptions, even before the occasion starts. "I always run late," means only when the occasion starts.
Forever doesn't work because forever means infinitely into the future (unless specifically said "forever into the past").
This is specifically related to modern usage. 500 years ago there were probably many words that would be an answer. However now those words mean more forever than eternal.
I am using this for "Truth [adverb] is all the following." and "I [adverb] infinitely strive." If you don't like the idea of eternal as an adverb being used for me (a finite being) striving, please only focus on the first example (or don't focus on any example). I am not asking a philosophy question beyond the English language. Specifically I am asking because I am creating an affirmation, and I want the affirmation to be truth in an eternal manor. My usage of the word is to negate the present tense of the verbs (to include the past, present, and future.)