Media & Disk Cache

Are you new to After Effects? Ram Preview time is more dependent on RAM than Storage. 

What version of AE are you using? What kind of system do you have? What is the version of your OS? What are the frame rate and frame size of your comp? Are you familiar with the Pencil Test/Ink and Paint workflow that most people use when animating or creating visual effects?

My standard workflow is to set up the animation, blocking, and timing of all of the elements with motion blur off, most of the time Fast Draft enabled, and no effects or only the absolute minimum number of effects applied to the layer. This is usually done with the Comp Panel Magnification Ratio set to 50% for HD comps or 25% for 4K comps, Comp Panel resolution set to Auto, and if necessary skipping frames. This is the Pencil Test phase. As soon as the timing is worked out and the blocking (where everything is) is worked out I move to the Hero Frames. These are the frames where the composite or the animation is most critical and finalize the effects, turn on motion blur, and carefully check a few of the critical frames to make sure that I am getting the look I want. This is the Ink and Paint phase. That's how Pixar, Disney Animation, and all of the other visual effects houses work. Nobody starts out trying to run ram previews on composites or animations that may take several minutes a frame to render. When the Pencil Test is OK and the Ink And Paint tests are OK, the project is sent to render.

You also said you allocated 13 GB of Ram to Adobe. This should be an even number, 8 or 12 would be a better number. Use 8 if you are doing motion tracking, Rotobrush, or any other operations that require AE to run in the Background using Dynamic Link. 

You also said your comp was one minute long. Generally, it is a really bad idea and incredibly inefficient to edit a video in After Effects. It is not an NLE. Most of your comps should be one shot, and that shot should only be something you cannot create in an NLE. If you must edit sequences in After Effects keep them to one phrase or one idea and do your transitions and editing in Premiere Pro. More than 90% of my comps are under 7 seconds because the average time between cuts in most of my films is less than 5 seconds. On rare occasions, when I don't need to make critical timing decisions based on audio or add sound effects, I will nest a few AE comps in a master comp and use that as a crude straight cut or short overlap transition between shots. I might do two or three of that kind of project a year. 

I hope this helps. Pencil Test/Ink and Paint is going to be the way to do most of your AE work until we get real-time previews with all effects, and even then, a layer-based system like After Effects, or a node-based system like Nuke is always going to be more cumbersome than a true NLE.