Hi and welcome from a fellow Dubliner. The answer is 'It Depends'.
Biggest question is is this the first of several trips, or do you want to finish something in this trip?
If you want to finish in that time, then you should fly into Santiago, get some transportation out to where you can walk from and head back in. O Cebreiro might be a good starting point; its a little further out than the required 100km.
What we did was to treat our first week two years ago as the start of our Camino, so we started the French way in St. Jean Pied de Port, and we walked to Pamplona. You would probably get further than we did as we only did 4 days walking.
From Dublin, we flew Ryanair to Biarritz, then got Express Bourricot shuttle to St. Jean ( there is also a train, but others will know the timing of that better.
From Pamplona we got 2 buses back to Biarritz. Transport timings somewhat determine how long you need at the start and end to get there and back, and how many walking days you will have.