Up until the last couple of years, the Atlanta Braves had been able to keep pace with the Dodgers in the National League. While it was (and remains) true that LA has more money to throw around on payroll, the Braves were still adding quality free agents, making big trades, and the pipeline of young talent from Atlanta's farm system was even more productive than LA's. However, the last couple of years have seen a bit of a shift that doesn't have easy answers.
Obviously injuries have played a massive role with the Braves' struggles as well as a few players deciding to fall off of a cliff. However, the bigger problem is that the Dodgers just seem to keep getting better and better and that has a number of causes.
LA has had a couple of prospect success stories (Andy Pages sticks out at the moment) and big money deals have been handed out to guys like Blake Snell, Tyler Glasnow, and the obvious example of Freddie Freeman. However, the bigger problem could to be that the Dodgers have the monopoly on top Japanese talent and there just isn't a great solution to that.
Dodgers' having their pick of the litter in Japan is an advantage the Braves have to figure out how to combat
At any point, the Braves could choose to spend more on payroll and be players for most of the same guys that LA seems to chase every offseason. It is also true that unlike the Dodgers who seem to hate trade deadline price tags, the Braves have been willing to make big moves at the deadline if the timing is right. Whether or not they actually do it, Atlanta has the sort of resources to compete with the Dodgers on the free agent and trade markets if they so choose.
However, the fact that the Dodgers have basically become the default destination for top Japanese players coming over to MLB is a big problem. While the Braves were never going to be in play for the services of Shohei Ohtani regardless (although they absolutely should have pushed harder given how much money that guy prints) either when he came to the big leagues or when he was a free agent, it was abundantly clear that both Yoshinobu Yamamoto and Roki Sasaki were essentially pre-destined to sign with LA.
See the problem? You have three of the players that are among the biggest reasons why the Dodgeres are still in the playoffs are players that the Braves had zero chance to sign. The last Japanese player of consequence that the Braves signed was Kenshin Kawakami and that...uhh...did not end well for anybody.
West coast teams are just always going to have a massive edge when it comes to signing big name players from Japan (or South Korea for that matter) because of the distance and marketing benefits and the Dodgers are king of this tier by a wide margin. The next tier are historic big market franchises like the Cubs, Yankees, and Red Sox who grab a big name here and there.
If a player makes it through those two tiers unsigned, the odds that they are worth signing at all are not particularly high. Unfortunately, there is not an easy solution to this problem. Sure, the Braves could dramatically overpay for Japanese talent, but that is asking for trouble and moving the team to the west coast isn't an option. Being more "aggressive" on the international market could help, but that is a heavily regulated market and breaking the rules in the name of "aggression" got the Braves in a lot of trouble before.
Maybe an international draft or changes to the upcoming CBA rules governing Japanese signings could change things. Whatever happens, it is clear that the Braves are operating at a pretty clear and massive disadvantage in what is becoming a more and more important market of players over in Japan.