The IRC lists several characteristics that might make a trust a "grantor" trust. One is if the trust is revocable. Another is if the grantor is the trustee. There are more.
Generally, a grantor trust does not need an EIN until it becomes irrevocable, i.e. after it stops being a grantor trust. That is usually upon the death of a grantor.
A trustee could certify an EIN. Only the grantor or someone holding a POA giving the attorney-in-fact sway over income tax matters could certify an SSN.
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