Ordinals with an indefinite article… Well, ‘a second\third etc.’ could be interpreted as ‘another’: “Greece, who finished behind Belgium in Group H, are aiming for a third straight World Cup finals…”
But why they have gone with the ‘a’ in: “The Republic of Ireland meet Denmark… as they seek to reach a first World Cup finals since 2002” doesn’t seem that obvious. (To me you can only have one first thing–the first, not one among ‘several firsts’.) What if they were seeking to reach “the first World Cup finals since 2002”?.. And that just leads us to a second question: “There is a first time for everything”–why is it ‘a first’?
I think ‘a’ means ‘another’ here as well but is applicable after 2002, which suggests that Ireland could have had similar occasions prior to 2002.
Now, logically, in a situation where there are first prizes for all those who score the maximum set by the event organizers, we can expect many firsts. So a competitor can win a first.