The first assessment shouldn't necessarily be looking for DCAP-BTLS, you are doing a much faster exam, looking for major life threats. Obviously airway and breathing compromises, and major bleeding. Broken wrist? Not something you care about on your first exam. Major bleeding from a wrist lac? Big deal. The initial assessment should focus on the pt's head (mental status, airway) and core (breathing), and a "bigger picture" look for the major bleeding (including skin color, pulse quality). I start by looking at my pt before I even have approached them. How are they positioned? Are they moving at all, making any sounds? Do I see any major pools of blood forming around them? Then going closer, are they breathing? Do I hear any obvious sounds (ie snoring respirations, gurgling). Do we need to open the airway? Does their respiratory rate appear adequate? Do we need to assist ventilations? Do they have a pulse radial and carotid? Rate feel adequate? Any injuries to the chest that may need rapid intervention (ie. flail segment, open wound). Major bleeding I need to control?
Only once those are all determined, and you know if you need to immediately "load and go" or "stay and play" do you move onto the full body assessment looking for DCAP-BTLS. On that second assessment, you do typically re-check everything that you checked initially, just to ensure that there haven't been any changes.
Here is a link to the most updated skills sheet