It is possible to watch Atlanta Braves games live online or on TV without an expensive Cable TV package. Usually these games are on Fox Sports South, but that may change depending on schedule, type of game or national interest.
The Atlanta Braves play most of their games on Fox Sports South, a regional sports network. Regional Sports Networks (RSNs) are not common on streaming services, but when they do exist they are usually only available for an additional fee.
Here are the live streaming services that carry Fox Sports South: Hulu Live, YouTube TV, AT&T Now.
The MLB also has MLB.tv, which live streams all out-of-market games for all teams. Unfortunately, Atlanta Braves games on here are subject to blackouts if you are within what is considered the team's "home region".
If you find yourself trying to watch a game on the MLB.TV that is blacked out, you will need a VPN to mask your location.