Does the filter have anti-drainback? If the filter drains back into the sump, it can often cause this sort of thing. Perhaps a heavier oil? I run Penrite HPR Diesel 5 (5W40) in mine. ('08 3.8L)
Because I can use the same oil in my CBR1100XX!
I found that mine would drink the Mobil 1 5W30, such that I would have to top it up before the next change. No such issue with the Penrite.
If it only happen at startup, it seems to be that it just takes a moment for the pressure to build up. If it starts coming on at other times, I'd begin worrying about the oil pump.