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.
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1. Really specific area of expertise that was needed by whoever was hiring them. "IT, software, ML" is very broad, but if you have a keen interest in data engineering for computer vision (random example), then you'll find people keen to talk to you. Try to narrow yourself into a high-demand niche.
2. Have a good "portfolio" of successful projects. I don't know your resume, but if you're stuck at getting to the formal interviews (i.e., getting screened out by automatic filters or recruiters), then you likely have a weak resume. This doesn't mean you need to work for a hot startup; work on side projects that stand out and show you can ship code/products.
Finally, a word of caution --- Tier 1 companies in the US are fantastic. Depending on how you define them, "Tier 2" companies have a huge range in terms of pay, quality, etc. and you might be in for a bad surprise. Make sure to do your due diligence on the company, the city, and the specific team you'd be working in.
Source: I run a data science careers site at https://phaseai.com/ -- feel free to reach out if you have questions.