How Can I Export a .pst from Exchange Online Without Purview?

If you're familiar with PowerShell, you can use it to export mailboxes to PST. I found this guide that could help: https://lazyadmin.nl/office-365/export-office-365-mailbox-to-pst/. Just a heads up, though, it does rely on Purview.

Since we back up all our mailboxes with Veeam, I just open it up and export the mailbox directly to a PST file from there. It's a straightforward process!

You can actually export a mailbox to PST using the Outlook client, but keep in mind that it only works for the mailboxes that you've saved locally. There’s a limit of around 12GB out of a possible 50GB, so that might not suit everyone's needs.

Honestly, the bigger question is why you don’t want to use Purview. Purview and eDiscovery are the primary methods for this type of task, unless you’re exporting via Outlook. In the past, there were options available through the admin center for hosted Exchange servers, but I don't believe that exists for Exchange Online now.