You might be interested in what's known as a DEX, or Decentralized Exchange. There are a few out there that service bitcoin purchases: https://defiprime.com/exchanges#bitcoin.
As far as Coinbase itself goes, you can save a point by placing your own buy orders via https://pro.coinbase.com/, but you still pay a small commission to the exchange to execute the trade.
Other exchanges like Gemini, Bittrex, BlockFi and Binance, have exchange credited tokens or coins that allow you trade at slightly lower fee levels, given you're willing to buy some upfront; it's like an escrow that gets deducted from whenever you place a trade.
I would also recommend CashApp for bitcoin only purchases, as they have reasonable fees and a great UI / purchasing experience. They also allow you to self custody.