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Just store what logs you need on a ram drive. The logs will be gone the instant the server shuts down and there is no way to recover them.
Downsides include : if any intrusion happens on the server, red team just needs to reboot it to wipe evidence.
If they have the root access typically needed to reboot a server1 they could also just wipe the logs without rebooting.
1: GUIs typically have a way to reboot without such privileges, but those are typically not installed on machines just used as servers.