The problem with the Eagles (and several other teams) is that they have a lot of players that have salary increases from 2019 to 2020. Players like Fletcher Cox ($11.9m in 2019 goes to 23.9m in 2020), Zach Ertz ($6.29m in 2019 goes to $13.2m in 2020), and Brandon Graham ($3.5m in 2019 goes to $13.2m in 2020) just to name a few. The total increase from 2019 to 2020 is roughly $80m, and the expiring contracts are only about $46, and the cap space is about 42m (I simulated through the preseason to get these numbers). This leaves you about $8m in cap space for the 2020 season (using the Eagles as the example, several other teams have a similar cap situation).
I am not sure of the best way to remedy this, but it is not a glitch or a problem with programming, it is a problem with the way the salaries are structured at the start of the first season. When you get past the first season, everything runs pretty smooth, but this is a reason I typically do a fantasy draft to begin my franchises (I also just like putting together my roster how I like).
It would be nice if in next year's game EA would tweak the contract offers so we can structure contracts in more than one way, and even restructure contracts.
I hope this is helpful in explaining the underlying issue, even though I can't really explain a satisfactory way of fixing the problem behind it!
Nate