How to create a Lightning Web Component without Salesforce DX?

You don't need SFDX at all (yes, even Salesforce CLI is not needed). It's fully supported by Metadata API.

Personally I'm using Illuminated Cloud plugin for deploying/retrieving LWCs but it's also possible to use Ant Migration Tool to do that (or other tool that's currently supporting deployments at API 45)

Add to yours package.xml:

<types>
    <members>*</members>
    <name>LightningComponentBundle</name>
</types>

Its available since API 45.

There is one limitation though as @Jayant Das mentioned. You cannot use Developer Console to create them.

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