I just checked, it seems that the cheapest way for someone to get to Guam is from Japan. Here’s what I would do to organize a competition.
1. Find a venue. Ideally this would be less than 250 dollars to rent for a day. I would recommend looking at (for venues): your school, your local high school, a church or other religious venue, a library, or a community center. You may have other connections to other spaces that would be cheaper, but that is my suggested list.
2. Talk to a delegate. As it seems that the closest one would be in Japan, I would try contacting a Japanese delegate. Some other options would be China or even Los Angeles if you can snag a deal. I know that flying a delegate out to Guam sounds hard, and to be fair it probably is, but you can probably offset those costs with registration fees.
3. The delegate will most likely help you work things out. You’ll find a date, sufficient flights and lodgings for the delegate, and then start to announce the competition. The delegate may even be willing to provide some funds simply to bring cubing to Guam.
I understand (and frankly, kind of expect) this endeavor to be in the future, but I hope my advice helps somewhat. Happy competing!