Actually Dane has suicidal tendencies but we as readers get to know as the story moves forward.
if memory serves right, maybe Dane thought there were more bombs set around the place. The big one just being the catalyst for the next ones coming up and Dane trying to stop them.
I think the reason it seems a bit confusing here is because fire fighters are not always bomb defusal expert to directly go into and handle potential bombing case, there are usually special team for that, just that Dane happens to have experience and think he can do the job. Also, the novel is slightly more clear at Grayson suggesting Dane to wait for more support to come instead of going inside alone with no equipment like Dane ia trying to do now. Dane actually has suicidal tendency which will be explored later through his past and repeatedly jumping into danger first and alone.
well that was an unexpected and breakneck tonal shift...also did the explosive not already go off? wouldn't it make more sense for dane to get involved because he's a firefighter, not because he knows how to disarm bombs??? and what is this business with dane saying it's fine for him to die since he doesn't have family??? that doesn't make sense for his character, it would make more sense for him to do it out of a sense of duty since we already know he's the type to run back into a burning house on the slim chance he can rescue a trapped dog. idk if this happened in the novel too (or maybe it was better written there??) but this really feels like the author didn't know how to move the story forward and just made something completely ridiculous up to raise the stakes out of nowhere lmao