CloudReady is intended for install. While you can use CloudReady fully in a liveboot mode, there is not much storage available because of the layout of CloudReady's partition table.
CloudReady is a relatively large OS compared to common linux distributions. In order to make sure that as many USBs as possible could be used as installers for CloudReady, we reduce the size of the installer image, which limits storage space. For the moment, this is not a feature which can be changed.
We encourage you to use CloudReady from USB liveboot for testing and experimentation purposes, but to move towards installation if you need to utilize more local storage over time.
Remember that you can always use a second USB drive, an SD card, or Google Drive to store files without keeping them on the limited live-boot USB.