According to Ayatollah Sistani you can give the amount as a loan to the needy person and then make niyyah on the night of Eid.

https://www.sistani.org/english/book/48/2309/

The same thing is mentioned in Tahrirul Wasila of Ayatollah Khomeini with notes of Ayatollah Khamenei .

It is not permissible to tender the Fitrah before the month of Ramadan, rather, according to the more cautious opinion, in all circumstances. Of course, there is no objection in its payment to a poor person and then accounting it for as Fitrah on the arrival of its time.