No. You cannot use first years choice to claim your niece. First year choice is for someone who is married to a US Citizen or resident alien as of Dec 31 of the tax year. Someone who is single is specifically excluded from making this choice. This is also for the taxpayer, not someone to be claimed as a dependent.
"Choosing Resident Alien Status If you are a dual-status alien, you can choose to be treated as a U.S. resident for the entire year if all of the following apply.
You were a nonresident alien at the beginning of the year.
You are a resident alien or U.S. citizen at the end of the year.
You are married to a U.S. citizen or resident alien at the end of the year.
Your spouse joins you in making the choice.
This includes situations in which both you and your spouse were nonresident aliens at the beginning of the tax year and both of you are resident aliens at the end of the tax year.
Note. If you are single at the end of the year, you cannot make this choice. If you make this choice, the following rules apply.
You and your spouse are treated as U.S. residents for the entire year for income tax purposes.
You and your spouse are taxed on worldwide income.
You and your spouse must file a joint return for the year of the choice.
Neither you nor your spouse can make this choice for any later tax year, even if you are separated, divorced, or remarried. The special instructions and restrictions for dual-status taxpayers in chapter 6 do not apply to you." Page 12 Pub 519
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