Yes, you can buy Bitcoin on a blockchain. All Bitcoins exist in their blockchains only. When you buy a Bitcoin, it is simply transferred from one blockchain address to another (yours).
If you are asking whether you can buy Bitcoins outside of exchanges, in a direct transfer, yes, it is called a Peer to Peer (p2p) trade. You can find P2P platforms across the world with just a simple Google search.
I myself typically buy and sell crypto directly on platforms like p2p and DEXs. They are much more private than exchanges.
