Can you migrate from a host that does not use cPanel

Yes. cPanel on both ends makes a move simpler, but it is not a requirement. Sites have been moved off Plesk, DirectAdmin, custom panels and plain servers with no panel at all.

What changes without cPanel on the old side

There is no single archive that contains everything, so the move is assembled from its parts: files, databases, email, and the list of what should exist when it is done. Each is straightforward on its own; the work is in not missing one.

The practical difference is time rather than difficulty. A cPanel to cPanel move of one account can be a single restore. The same site from a bare server is a handful of steps.

The parts that need attention

• Email. The most commonly forgotten piece. Copying files and databases moves the website and leaves years of stored mail behind. If mailboxes matter, they have to be moved deliberately, which is covered in moving email without losing messages.
• Cron jobs. They live in the old panel and do not travel with the files. Anything scheduled has to be recreated.
• Server level configuration. Custom PHP settings, rewrite rules outside the site directory, or anything a previous administrator put in a server config rather than in the site.
• Certificates. Usually easier to reissue than to move, particularly if the key cannot be exported.

Windows and IIS

Moving a site from Windows hosting to Linux is a migration and a platform change at once. Static sites and most PHP applications move without trouble. Anything relying on ASP.NET, MSSQL, or Windows specific paths does not, and that has to be established before the move rather than discovered during it.

If you are not sure what a site runs on, that is the first thing to check rather than the last.

Sites with no panel at all

A plain server is often the easiest source, because you have shell access and can produce exactly the archive and database dump you need without fighting an interface. The move then looks like any other file and database restore.

What to do first

Inventory before you touch anything: every domain, every subdomain, every database, every mailbox, and which of them are still in use. Estates almost always contain sites nobody has looked at in two years, and a migration is the right moment to decide whether they are worth carrying.

The question of moving versus rebuilding is worth asking per site rather than for the estate as a whole, which is covered in deciding whether to migrate or rebuild. What access is needed once you have decided is in what access a migration needs.