I guess it kind of depends on the scenario. Are you getting dropped right into a combat zone or are you getting initial contact in the form of merchant traffic? Hopefully it's the latter.
I usually do my first scan with the sphere and hull arrays, because with those I don't have to worry about a false direction, and because it helps me pay attention to closer contacts first. If I start at PD, I'll throw the ESM antenna up and mark those because that's instant classification (periscope too if something is loud, on the surface, and not radiating). The towed array comes next, and I'll intentionally seek out the contacts I already have first. This reduces the time spent on the TA scan because I already know what bearings to get them on and which is the real contact, so in essence for every S/H contact I have I eliminates work on two TA contacts. Also, it helps with tracker assignment, because the trackers that get removed to follow newer contacts will be those that already have a sphere/hull tracker. Once all TA contacts on my initial course are marked, I'll turn to clear the bow baffle and eliminate false bearings, scan, cross the layer, scan, turn again, and scan again.
I think in a situation with a moderate number of initial contacts (like 4 or so) I'll have situational awareness established in ~5 minutes.
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