The easiest thing to do with the first mission is just to disable LWAMI for it. The Oscar has a towed array in LWAMI, but not in stock DW. The towed array is what will sometimes detect you from the start of the mission.
The other option is just to hope for a better spawn.
With the P-3, I'm not too sure, but you might be able to avoid being engaged if you keep your radar off and avoid flying too close to anyone. They'll detect you on radar but they won't classify you unless they have you on ESM or visual.
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