I mean, if you set up your os on an encrypted ram disk, then set it to restart when the server rack door was unlocked/opened and didn't leave a backdoor for yourself to remote in, you could have a situation where you entirely lack the capability to give them access to anything before that moment. A skilled hacker might be able to get in through an exploit or do something crazy with cryogenics to read the memory at the time of shutdown, but a quick restart would overwrite most of what's in memory and scrub that
Legally, there's not much better defense than "I'm sorry your honor, I can't provide access to the running system in the same way I can't un-shatter a smashed mug". If someone shows up with a warrant, you could explain that it'll wipe itself if they open or unplug it, and it might've done so already. Then you guide them to it, hand over the key to the server cabinet, and let them decide to open the cabinet and destroy evidence so they can take it with them. Or they can take you at your word, and give up.
Court orders can't break physics, and as a VPN your reasoning for setting up the system like this is to make your service more appealing to customers - the purpose is not to aid in a crime or destroy evidence, it's just the normal course of business.
The same way that most companies wipe their emails after 30 days - yes, it potentially destroys incriminating paper trails, but that's just a side effect of the security policy you've had all along
Granted, there's probably some sketchy sealed laws they could use to force you to backdoor your own system moving forward, but you can fight that as it's undue hardship. It requires a non-negligible amount of work and would make your product less competitive
They might win in the end if they keep pushing, and even might be able to order you to "keep up the canary paper" (meaning keep claiming not even you have access to the running system), but more likely they'd get a warrant for your customer financial records and try to find an easier path to find what they want elsewhere
