Someone suggested I divorce my first wife first so I don't need polygyny permission. Is that right?

No; divorcing a wife merely to avoid the procedure is injustice wrapped in a trick. Talaq (divorce) is not an administrative tool. It breaks the bond, threatens maintenance and shakes the children's hearts. If you plan to take her back (rujuk) after marrying another, the trick adds yet another injustice. Allah says: “do not retain them to harm them, so that you commit injustice” (Surah al-Baqarah 2:231). If you are truly able and need polygyny, take the lawful and honest path. If not, perhaps the answer really is not polygyny. Talk to a counsellor before making a decision that cannot be undone. See talaq.