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While it is unfair, it is not illegal to implement the policy you describe. It is not illegal because employers are not required to offer any paid time off at all. Since they are not required to offer this job perk, they are free to offer it on any terms they desire, provided those terms do not discriminate on the basis of a legally protected trait, such as race, religion or gender.
Here, it appears they are offering paid time off on the condition it does not accrue until the anniversary of the employee's start date. An employee's start date is not a "legally protected trait" and so that is a lawful basis for determining when PTO accrues. Certainly, the result is unfair in your particular instance and I don't blame you for being frustrated. But the law does not require your employer to be fair, it just prohibits them from implementing policies which discriminating on the basis of legally protected traits.
So, I'm afraid all you can do in this circumstance is attempt to reason with your employer. Beyond this, you would not typically have any recourse.
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