Do you have a local bitcoin ATM around where you live? You can use that to fund your BTC wallet first and then transfer it to your exchange.
Not around where I live, but about 1 hour away in one of the cities in Australia. They charge 4% fees but I don't really know how competitive the rates they give are, compared to the exchanges. I'm presuming that the ATMs don't really give a good rate, therefore it ends up a lot higher than 4%. Am I right in assuming this?
Otherwise if 4% is all they change, then it's exactly the same as Coinbase exchange.