I also left for US mid career. I agree with what everyone is suggesting here.
1) A data scientist with data engineering skills is much more valuable to most companies. If you don't already have any, build a couple of data engineering & data science projects on your own, and note any engineering trade-offs for DE projects.
2) Learn about how interviewing works in US, especially at FAANG companies. Give yourself ample time on this task. Join US based online study groups, and this will also help you expand your network.
3) Network aggressively with tech people in US, and see if anyone you know can help you submit your resume to recruiters there.
Optional 4) Finally, the most straight-forward path that I'd recommend is to study at a US based DE, DS, ML, AI bootcamps, or fellowship program. But I can understand that you may feel like it's not a productive use of time since you're already a DS. Also, may not be a great option when you can't go to class in person in US.
In any case, steps 1-3 are definitely the most important for what you're trying to accomplish.