I will take your silence to mean that you are not at the top of your field. If you are, here is a link to the green card where you can self-petition:
Even for an O-1 visa, you still need at least an agent to sponsor. Here is a link to that:
If not, then you will need to find an employer willing to sponsor you. I understand that the companies that you have approached are not willing to do so unless you already have the visa available. That just means you have to keep searching. There are companies out there. Of course, you may not end up working in the city that you preferred to work, but sometimes you have to sacrifice for the bigger picture. Here are some links to some websites that may be helpful:
If you are an educator, of course you need to look at schools, colleges and universities, but that has a benefit as well because you could apply for your H-1B at any time and not be subject to the cap/lottery.
Let me know if you need anything else, but please do not forget to rate me positively. You can do that by clicking on the 3rd, 4th or 5th stars if you see them, or the smiley faces if you see them. If you do not see the stars or smiley faces, please scroll to the top of the page to see them or click on my name and they should come out. Also, we do NOT finish just because it says "Rate to Finish" or something like that. Your question does NOT close and you can continue to ask questions without additional charge on the same question thread even after you leave a positive rating. Thank you for your understanding!