Is there a way that I could use an FTP on my wordpress via kubernetes google cloud?
You usually update the container image, as changes will be lost otherwise.
That is the best practice and recommended approach. Doing that to modify the container is usually a practice that will hurt you in different ways.
Are you sure you want to add an ftp container to the pod? Why? 
I thought its the same with some server. I read about it and gives me an Idea that it uses git for transferring files and when it is on the live site it is now a read only. Am I right?
Oh I forgot why I want to have ftp access because I want to upload the file compressed and uncompressed it on live so I can restore my wordpress backup files with database. And if has permission I would change it back. I dunno if this possible.