The Verdict: Not eligible
You cannot naturalise from abroad: you must first live in the Republic for five years on a permission that counts. Check descent and marriage first, then look at an employment permit as the way in.
Residence comes first and the application after, so the real question now is how to arrive. The usual way in is an employment permit, ideally a Critical Skills one. A working holiday suits some nationalities and ages, and the Start-up Entrepreneur Programme suits people with capital and an innovative business.
Two routes may be faster. A parent or grandparent born on the island of Ireland may make you a citizen already or entitle you to register, with no residence at all. Marriage to an Irish citizen shortens the residence needed to three years.