Adobe AI and PS are Adobe Illustrator and Photoshop. Professional software at a professional price. They might offer an introductory free month or week. I don’t know. Illustrator is a vector drawing program. Basically it draws in lines and shapes. Photoshop is a pixel drawing/ manipulating program. For the glowforge you will be designing in both types of programs.
A free alternative to Illustrator is Inkscape and I think Gimp is the go-to free alternative for Photoshop.
As the glowforge will be able to scan from hand drawn work you can try just drawing your designs on.