Paul talked about how God's goodness can lead people to turn back to him. Unfortunately, some people at first are resistant to God's goodness, and some people don't even plan on turning back to God in the first place.
In fact, Paul talks about how "in accordance with [...] hardness, [we] are treasuring up [...] wrath" (2:5). The "accordance" part implies that people have varying degrees of hardness -- some are mildly resistant while others basically do not want to turn from evil, at all, ever. Additionally, considering that God's wrath is his passion to stop sin from ruining lives, the storing of wrath is referencing how the more we sin, the more reasons God has to show that we are not good. Sin is kinda like garbage -- the more garbage there is, the more stinky the area is, and even a little bit of garbage ruins the area.
Then Paul talks about the "the day of wrath and revelation of the righteous judgment of God", where God will "render to each one according to [their] deeds" (2:5-6). Those who are good can get eternal life, glory, honor, and peace (2:7,10), but those who are bad could face "indignation and wrath, tribulation and anguish" (2:8-9). The Greek word for "indignation" (Strong 2372) also conveys passion, but from the connotation of "outburst", it is more sudden, which makes sense because of how sudden the confrontation could be. Tribulation and anguish could come from multiple factors -- confronting own mistakes (similar to real-life cases of regret), realizing that you let down God, getting overwhelmed by God's power and seriousness, or even just meeting God that they rejected.
As a side note, Paul talked a few times how judgment would apply "of the Jew first and also of the Greek" (2:8). Paul may be referencing how Jews had been under God's close supervision first (or even the Jews who lived before Paul's era).
Considering the bad actions that we all did and how God does not like bad actions, the report isn't going to look good on us. But the good news is that God offers a solution, and Paul will talk about it in the next chapter.