migration – Moving a WordPress auction from staging to live after maintenance without resetting timer

I hope this is clear enough, and thanks in advance:

I see a great deal about migrating from staging to live on StackExchange, but not quite my particular issue (at least not that I have found). We have an auction site with about 62 plugins in use and a fair amount of custom code. We’re trying to do maintenance and update testing on the staging to keep the live site from being affected. However, one issue that we have is that by doing so, the auction plugin timer gets out of sync and therefore affects the auctions. I suspect that I already know the answer since these are based on the system clock, but is there any way to push an auction site in the staging environment to live without affecting the time, or is there a method to globally set the timer via Linux? We are using CentOS as our server, which is a dedicated server. Here are the other details:

WP 5.6,
Theme ‘Base WP’ with a child theme 2.18,
Woobuilder blocks 3.6.0,
Auctions for Woocommerce by WPInstitut 1.3 (updating to 1.5),
Woocommerce 4.8.0 (updating to 4.9.2),
Wordfence Premium 7.4.14

I won’t list the other plugins, unless necessary to solve this issue, but there are many other updates to manage too.

The domain is https://legacyguitars.com and I am aware that there are other issues, I am just trying to solve this particular issue here.

Thanks again.