To answer your question: essential oils do have mild hair growth stimulating effects, but they are very concentrated and thick, and may cause scalp oiliness and other side effects in the process. Once you stop the oils, the effects are also gone too.
Minoxidil does not always have initial hair fall. It is an FDA approved medication for hair growth, and has foam versions to prevent scalp oiliness.
Minoxidil is still way superior than essential oils. If you are having female pattern hair loss, I highly suggest for you to go for the tried and tested option.