There must be other ways of doing this. I have heard of countless people moving to the United States, and they were definitely not all refugees or relatives of American citizens.
How well do you know those "countless people"? Most of them probably did have US relatives, but you just didn't know it. The vast majority of legal immigration to the US is family-based.
And how many of them immigrated permanently and legally? Some of those "countless" individuals probably are in the US only temporarily with a student visa, and some others entered with a tourist visa and overstayed.
It is very difficult to get an employer to sponsor you directly from outside the US. A more typical path to employment-based immigration is to first study in the US with a student visa, then upon graduation get hired by a US employer with a temporary work visa such as H1B, then convince the employer to sponsor the green card. And then you have to hope they don't lay you off before you reach the final stage of the process, otherwise you have to leave the US or restart the green card process from scratch with another company.
Another path is to work for a multinational corporation that has branches in the US, and get them to transfer you to the US. That's how I got my first work visa. Then I changed jobs to another company that sponsored my green card.
If you have "extraordinary ability" in the arts, sciences, business, or sport you can self-sponsor your employment-based green card. That's how many famous actors and singers, top scientists, world class athletes, and big businesspeople have immigrated.
I forgot to mention the EB5 investor green card, which is another route for self-sponsored employment-based immigration. It requires you to invest at least US$1 million ($500K in certain designated rural or underserved areas) in a business and create at least 10 US jobs.
But the bottom line is that for most people there is no realistic avenue to immigrate to the US. If it were realistic for most people, the US population would be like India or China. Legal immigration to the US is only about 1 million per year.