You can't just apply for a Green Card. You have to be sponsored either through family or an employer. To do it through an employer you have to be eligible for a
TN Visa, and if not then you have to start by changing careers or find someone to marry
If you find an employer willing to hire you and sponsor you for a TN, you can come and work. You can try to go from TN to Green Card, or you get the company to sponsor you for an H1-B (if you can win that lottery), then go H1 to Green Card route. They just accepted a whole ton of applications which may backlog the processing in a different part of the processing chaing
Keep in mind, it takes 5 years or more, and losing a job can cause problems.