I'm Greek and she has both nationalities. Proposed me to move in states. Best option to be eligible to work there?
To get married 60 days after your arrival in the US and file for agreement card which you should obtain within 30-40 days.
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There's a K-1 fiancée visa, which authorizes you to be in the U.S. for 90 days to get married and file a Form I-485, Application to Adjust Status, to become a permanent resident.
Theoretically that entitles you to a 90-day employment authorization document, but in practice it takes 90 days to get the card, it's worthless. You won't be authorized to work until about 90 days after you file the Form I-485.
So if your main concern is work authorization, then you can either apply for the K-1 fiancée visa before marrying or the spousal immigrant visa after marrying. Of course, there are other issues to consider in deciding between these two visas (e.g., timing, filing fees, whether you prefer to marry in the U.S. or abroad, etc.)
You cannot based on your facts. You might be, if the circumstances change, like you would get married and decide to permanently relocate to the USA. Otherwise, you would probably need to continue staying in Europe.
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You have several options available depending on what you want to accomplish. If you will need to work immediately upon arrival (or as soon after arrival as possible), you should consider the K-3 process and get married in Greece. Adjustment of status might be an option depending on your factual circumstances. You should consult an immigration attorney who can explain the various options and each one's pros and cons.