It does not mean you will always have to wait very long time for first confirmation with low transaction fee rate then low transaction fee. It depends on mempool status and if mempool is clear, you can get very quick first confirmation within 1 or 2 block. If you are lucky enough if a time between your broadcasting time and next block time is very small, you will get first confirmation even after 1 to 2 minutes.

Watch mempool status and compare unconfirmed transactions in mempool, their fee rates and yours. https://mempool.space/