If something on the page expires sooner than that pages cache then you will end up in this situation or an analogue/equivalent situation.
So in the strictest sense the answer is a hard no.
Either the nonce expiration has to increase, making the nonce less secure, the cache has to decrease so that the things being cached don’t become stale, or that page/page fragment can’t be cached. Everything else involves fundamentally changing what you’re doing, e.g. pulling the form in via JS, using an iframe or embed of some sort, not using a nonce, etc
Note as well that WP doesn’t just check if the nonce is currently valid, there’s a grace period where it also checks the value the nonce would have had previously so that stale nonces don’t just instantly expire.
Depending on your use case, the use of nonces here might not be correct, e.g. if it were a form int he admin area or for a privileged/logged in user to perform an action then a nonce is appropriate. But for lets say a contact form that has no authentication a nonce may not be appropriate. Gravity Forms for example does not uses nonces unless there are restrictions around the form or it requires user login.
As with most rules, PHPCS is there to catch issues and be a tool to better your code, but you shouldn’t blindly implement its recommendations without considering the context. You can silence it with a comment, just be sure to add your own comment explaining why you aren’t using nonces and what you’ve done instead to protect the form ( e.g. captchas ).
As for AJAX, it defeats the point of the nonce since now anybody can query to get the nonce from AJAX without opening the page, eliminating the point of having the nonce in the first place to ensure that the submission of the form came from that specific place. You also then run into the problem of cached AJAX entries, and that you might need a nonce to securely retrieve it putting you back at square one.