Updated June 15th, 2019.
Get your old emails out of the Mac Mail app’s Inbox. The fewer items in the Inbox, the faster the Mail program displays them. Just make a new “Mailbox” (Mailbox menu, then New Mailbox…) and drag a bunch of your old mail into it. You might try making a Mailbox for “2018 Email” and another for “2017 Email” and so on.
When you make a Mailbox, you get a choice of where to make it. If your only option is “On My Mac,” then that’s what you do. But if you have any other option, the odds are good that the other option will be better. For example, if you have an option to make the folder in iCloud, do that. If you have an option to make it on your Exchange server, do that. This way, the Mailbox will live on the server, and will be available to your other devices (iPhone, iPad, another Mac).
Note: Apple calls it a “Mailbox” while you may think of it as a “folder.” It’s the same idea, no matter what you call it, although they are not exactly the same thing. Here, you want a new mailbox.