If you have the option to recreate the phrase Even if it takes forever and use multiple words you can acceptably use either whenever or however. For instance:
- "Whenever it happens, I am going to speak English like a native."
- "However long it takes, I am going to speak English like a
However, if you tried to use only a single word, either whenever or however, then either would in most cases sound cluncky to a native ear. Also, however changes meaning when used as a single word to start a sentence. In this case, however signifies a contrast. I can say:
"You predicted I will never learn to speak English well. However, I am going to learn to speak English like a native. Then you will see how wrong you were."
But I couldn't use "however" as a single word to start a sentence if I wasn't making a contrast. In your example, you cannot know that something exists to make that contrast; therefore, however as a single word is not appropriate.
Whenever can be used as a single word at the beginning of a sentence and when so used can retain its meaning of "no matter when" or (used informally) "at an unknown or unspecified time" - both definitions from Collins.
It's more common by native speakers to use a single word whenever at the end of a sentence, such as "I'll do that whenever" the same way one can say "I'll do that happily." But as always allowed in English, the adverb can be moved to the beginning of the sentence. It is possible to say, "Whenever, I'll do that" just as it's possible to say "Happily, I'll do that."
There's a recent hit song by Shakira that uses whenever in this way:
"Whenever, wherever, we're meant to be together."
Shakira's not a native English speaker but I think this line sounds acceptable to a native ear.
Also commonly heard in English is the single word whenever when the rest of the sentence is understood. I doubt any native English speaker would have a problem with this dialogue:
A: "When should I pay you back?"
But technically the full sentence is "Whenever [you pay me back]." So while most native speakers may not be accustomed to hearing whenever at the beginning of longer sentence and, thus, it sounds wrong to them, they actually hear whenever used in this way with understood sentences all the time. Let's try again:
A: "When are you going to to speak English like a native?"
Again, no one would have protested this use because this form is so commonly heard. But the full, understood second sentence is "Whenever [I am going to speak English like a native]." Which means that had you said the full, understood sentence, you would have been correct even though it might have grated on native ears that are not used to hearing the full, understood sentences.