Can I register for 10DLC without an EIN or LLC, as a sole proprietor?

Yes. On the brand step of the 10DLC registration there is a Sole proprietor option. A sole proprietor registration uses your own name and your mobile phone number instead of a social security number, so the process is slightly different but basically the same, and you can do it straight away. Low volume as a sole proprietor is $10 a month. Registering as an individual is not easier than as an LLC: the same rules about your website and use case apply.

If you want the registration under your LLC or corporation, you need a legal business entity, its address and an EIN. You must have the entity before you can get the EIN, and you can usually get an EIN online, often the same day. If you do not have them yet, you can use the Sole proprietor option or wait and do the 10DLC registration later.