Congrats on the move! Some basics for jobs :
(1) look at how a typical US resume is formatted (especially, brief) and follow that. Make sure to put somewhere at the top that you are legally authorized to work/green card holder
(2) a lot of job applications go through a software filter first. Make sure your cover letter and resume include the key words of what they are looking for, per job
(3) are you on LinkedIn? There is a lot of job “spam” through LinkedIn but it can also be very useful. I do know people who have been recruited for good jobs through their LinkedIn profiles.
(4) be patient. The jobs market is big, but there are also a lot of applicants. It can take new immigrants many rounds of sending in applications before someone bites. The good news is that once you have some US experience, it becomes easier to get on to the next job.
(5) Be flexible. Many new immigrants have to take a step back on the career ladder to start working here. If you’re lucky you won’t, but you may need to.
Good luck!