3 options spring to mind.
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you could use the DNS challenge (that way you don’t need to upload anything to your site). certbot doesn’t support the DNS challenge currently but certainly the bash and go alternate clients do.
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You could upload the tokens to your site via FTP to verify ownership of the domain, and obtain a certificate. Again this is easiest with one of the alternate clients I think.
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since you currently using http only, just transfer the site over as http only, then create the cert once on the new server.