Yes, you normally just lift the platter / sub-platter off the top of the motor. At least you've got a good look at the thrust face that the ball on the bottom of the spindle runs on (that one looks like nylon, some players use lapped and hardened steel, even ceramic).
It looks as if there is a reasonable amount of wear, which will cause more the ball surface to thrust face contact, but it shouldn't squeak. Check that is still clearance between the flat end of the shaft and the thrust face (ie. just to ball in contact), just to make sure the platter isn't running too low in the deck.
The more likely place for a squeak is the bearing bushes around the sides of the shaft if they are running dry. Look for any scores in the shaft that might indicate abrasive particles embedded in the bearing bushes. Also check for side play in the spindle (wobble at the edge of the patter). The only other potential sources of a squeak would be corrosion on the pole pieces or magnetic swarf on the inside surface of the magnet, rubbing against the pole pieces and possibly, any parts of the auto-return mechanism rubbing against the rotating parts (I'm not clear how this works as I can't see any gear or cam).
The spindle bushes probably need some lubrication by now. I would normally suggest oil, but this is likely to run down the spindle and contaminate the plastic compatible grease on the thrust plate, possibly leaking out of the bottom of the motor, around the metal cap. In this case I would suggest a very light smear of clean Lithium based grease on the surface of the spindle. Also re-distribute the grease on the thrust plate back to the center, where the ball runs.
Keep everything scrupulously clean on re-assembly. Go around the inside of the magnet with adhesive tape to collect any magnetic particles, check the pole pieces, clean and lightly lubricate the spindle and re-assemble.