Yes, you absolutely can create nested directories without the -p option, but it requires a slightly different approach.
When you don't use -p, the mkdir command expects that the parent directory (or directories) you're trying to create a new directory inside already exists.
So, to create maze/twisty/little/passages without -p, you would need to create each level of the directory structure individually, in order:
mkdir maze
mkdir maze/twisty
mkdir maze/twisty/little
mkdir maze/twisty/little/passages
If you try to directly run mkdir maze/twisty/little/passages without -p and if maze doesn't exist, you would get an error like mkdir: cannot create directory 'maze/twisty': No such file or directory.
The -p option is a convenience that automates this step-by-step creation of parent directories.
Do you want to try creating a nested directory structure without using -p to see how it works?