I think the OP may have just made a mistake. As a native speaker, his sentence is wrong. "It took" is perfect paste tense. I think their intent was to say "It will have taken, (future perfect), or "it will take" (simple future).
"Even if the vaccine is available, it will take" is wrong because the vaccine is not available. That means you need "would" instead of "will", and ideally a past subjunctive verb in the if-clause. "If it were available, it would take time to distribute."
https://en.wikipedia.org/wiki/English_conditional_sentences#...