Enumeration
Run linpeas first for a broad sweep, then manually verify the interesting findings: automated tools flag a lot of noise.Sudo Abuse
sudo -l shows what commands you can run as root: check every result on GTFOBins for a known escape.
SUID Abuse
SUID binaries run as their owner regardless of who executes them: anything non-standard owned by root is worth checking on GTFOBins.Cron Jobs
Look for cron jobs running as root that call scripts you can write to: rewrite the script, wait for the next execution.Writable /etc/passwd
If/etc/passwd is world-writable, you can add a new root-level user with a known password hash.
Capabilities
Capabilities grant specific root-level privileges to binaries without full SUID:cap_setuid+ep on an interpreter is effectively root.