"It will take" would work fine if he had said "Once the vaccine is available, it will take...", because that doesn't imply the vaccine is available now.
"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."
"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#...