Here are two different strategies for AP farm and level up Materia fast in FF7 Remake.

As long as you have Materia slotted on a weapon or armor of an active character, it will gain AP - which works like EXP but for Materia. Once this AP is maxed out, you will be considered to have Mastered that Materia. Mastering all Magic (Green) Materia is one of Chadley's Battle Intel Reports, so you'll need to do this to progress.

How to Farm AP and Level Up Materia Fast

I recommend waiting to actively grind Materia until after the credits roll, since you'll get a 2x bonus to AP earned! There are two methods I recommend to gain AP fast:

Repeat the Two-Person Team vs High Flyer mission in the Shinra Combat Simulator repeatedly (redoing the battle when you reach the final fight)
Repeatedly defeat the enemies just outside of the Shinra Combat Simulator, since they respawn right next to a bench.

There are a couple of fast ways to AP Farm in the end game of Final Fantasy 7 Remake, but I highly recommend to Chapter Select over to Chapter 17, and play through the first 5 minutes or so in order to get to the Shinra Combat Simulator. Load up Cloud with a Fire + Magnify materia combo, a First Strike Materia, and then load up Barret with another First Strike and fill up the rest of the slots with whatever materia you wish to level up. Attach the AP-Up Materia in a linked slot to the Materia you want to level up the most, as this will provide an AP bonus.

Then choose the Two-Person Team vs High Flyers mission.

You can instantly clear the first mission against the group of bugs with a quick triple slash, and the rest can be completed almost as easily with a combination of Cloud using Firaga, and Barret alternating between using his Maximum Fury skill, overcharge, and basic attacks.

The only tricky one is the last fight against the Drake, which will reflect magic attacks back at you. If you have the Gil to spare, itís often better to just give up this fight and retry the mission because you keep all the AP you earned up to that point, and all you really give up is a paltry 400 Gil.

Fight Outside the Battle Simulator

If you donít have the Gil to spare, you could also fight the enemies just outside the Shinra Battle Simulator in Chapter 17. These guys respawn after a short while, and thereís a bench nearby too, so you can just get in a rhythm of nuking them with fira spells, running back to sit at a bench and restore your MP, peeking through the window to see if they respawned, and then doing it again, and again, and again. Itís a bit slower, but it doesnít cost any Gil, and since you can use three people at once, you can fill up materia on three characters at once.