When attempting to register a .US domain with GoDaddy, there are three options presented: - being a citizen of the USA, - having a business there, - or having origins from there.

I do not fit into any of these categories.

Are there any alternative methods for achieving this?

You can still register a .US domain through GoDaddy even if you don't fit into the three standard categories. One alternative method to achieve this is by partnering with a US-based individual or entity. You could collaborate with a US citizen, a US-based business, or an organization with roots in the United States to register the domain on your behalf.

By forming a partnership, you can establish a legal connection to the United States that allows you to comply with the registration requirements for a .US domain. This partnership could take the form of a joint venture or a formal business relationship, where the US-based party holds the domain registration while you maintain operational control over the website and its content.

It's important to ensure that any partnership or agreement you enter into complies with the domain registration policies and legal requirements set forth by the domain registry authority and GoDaddy. This may involve drafting legal contracts or agreements to define the terms of the partnership, including rights and responsibilities related to the domain registration and usage.

By leveraging your expertise and forming a strategic partnership with a US-based entity, you can navigate the domain registration process and secure a .US domain for your online projects, opening up new opportunities to reach audiences in the United States and beyond.

To register a .us domain, the registrant must provide valid contact information in the United States or its territory. Foreign entities with a US office are also eligible, but they need to disclose their country of citizenship. Additionally, the domain's DNS must be hosted in the USA, and transferring the domain to a third party requires written permission from the registry.
It's crucial to ensure compliance with these requirements when setting up a .us domain. The importance of accurate contact information and the restrictions on domain transfer underscore the need for careful consideration in choosing and managing domain registrations.

This is my initial exposure to DNS and the concept of obtaining written permission from the registry, but there's a requirement to be located in the United States. I haven't encountered these types of inquiries from Internetbs before, as far as I can recall.
In other cases, they request information on the intended use of the domain (commercial/nonprofit/personal/educational/government) and the registrant's status (citizen/green card holder or property/business in the USA).