Having started 4 days before the previous PoA, here's what I can say about my experience.
I don't think it is doable as a free player *on a new account* (edited).
I put a bit of money (10€ or so to get a starting pack and the silver card) in the game to get a good start. That allowed me, among other little things, to unlock the koban path, making the event much more accessible. The additionnal rewards were a great help each time for the next step. I finished with slightly less than 2 days left.
Daily contests are also a great source of resources for the PoA, especially the Combativity points.
I did manage to unlock access to the champions and started to attack them. I was worried it would not work out but I read here the advice about putting very bad items and setting the girls out of the favored positions. Although it was long waiting 15 minutes between each fight, crippling myself was enough to avoid the 24 hours downtime until I had finished the corresponding PoA step.
That said, I'm not sure the same is feasible with this PoA. some numbers have increased and a few rewards seem out of sync with the next step.
Edition :
About the Tower and the Leagues : getting quickly to W2 hurts a lot.
Try not to do better than 16th for some time, in order to have more beatable opponents. It's one thing that's hard on starting players. You try to rush because it gives Xp and end up in a bad position for at least a week. And getting back to W1 means a week without Tower fights, not compatible with PoA.
I just remembered something : the bit I paid wasn't enough to get the kobans for the paid path. I also did explore the "Sex friends" page (available in game through the menu) to get the kobans I lacked. It's up to you to see if you want to go that route or not.