Yes, many applications are currently deployed on the Hedera mainnet, generating millions of transactions per day. However, we recommend starting application development on the Hedera testnet, before migrating to the mainnet.
To get started building on the Hedera testnet or mainnet, please visit the official developer documentation: https://docs.hedera.com/
The Hedera developer quick-start guide can be found here: https://docs.hedera.com/guides/getting-started/introduction