How to query dates in different timezones?

I have a table and index in a PostgreSQL 10.18 database:

CREATE TABLE some_table (
    expires_at timestamptz
);
CREATE INDEX ON some_table(expires_at);

Is there a way to write this query in a way to use the index on expires_at?

SELECT
    *
FROM some_table
WHERE 
    TIMEZONE('America/New_York', expires_at)::date
  < TIMEZONE('America/New_York', NOW())::date
LIMIT 5;

America/New_York is added as an example, this query is run by using different time zones.