How can I migrate from a server with cPanel AutoSSL to one using Let’s Encrypt without an interruption to my SSL coverage?

I’ve currently got a live website which is set up with it’s SSL cert being provided by cPanels AutoSSL feature. I’m going to be moving my website to a VPS that is provisioned by Laravel Forge and set up to use Let’s Encrypt for SSL certs.

On the new server, I cannot activate the Let’s Encrypt certs because my domain is not pointing at those new servers. However, if I point my domain first, then I run the risk of users hitting my website without a valid SSL cert and seeing a warning about the site being insecure.

Is there some way I can avoid this situation – perhaps by transferring my existing cert to the new server or somehow setting up my Let’s Encrypt cert despite the fact that my domain is not pointing at the new server yet?

I would like a seamless transition where I point the domain at my new server and it already has a valid SSL cert so my users aren’t seeing security warnings.

Thank you!