Maxing your confidants out in a single playthrough of Persona 5 is a difficult task. Social stats gate many Confidants, making them harder to get in the early parts of the game. Since social stats carry over into New Game Plus, maxing Confidants on a second playthrough is far easier.
In a first playthrough, you must spend every possible moment either maxing your stats or working on a relationship. Upping your social stats (Kindness, Knowledge, Guts, Proficiency and Charm) will happen over time naturally, but you should also work on them individually.
Getting the most out of each session with a Confidant takes dedication. You must be sure to visit the Velvet Room and grab a Persona that has a matching Arcana with your Confidant. For example, bring Pixie (a very early game Persona) with you when you hang out with Ann, as they are both aligned with the Lovers Arcana. This will cause your relationship with Ann to grow faster than normal. Details on every Confidant and a greater explanation of the Arcana matching are available in our Confidant guide.
Spend the early parts of Persona 5 (when you only have a few Confidants at your disposal) leveling up your social stats. As the game goes on, it is easy to get overwhelmed with choices about who to spend time with. Max your early Confidants as soon as possible so that you can focus late game on characters like Haru or Iwai.
We have a daily walkthrough of the events of Persona 5 already, but if you want a detailed breakdown on how to optimally spend every day for the maximum benefit, check out this great and detailed breakdown on GameFAQs.