It could be just a pressure relief valve problem. It has a ball bearing and a spring on it and as well as stopping oil pressure getting to high it also stops oil running out of the oil ways back into the sump.
There is also an o ring around the oil pick up pipe where it goes into the block that can cause oil pressure problems. These 2 things are eassy to change with the sump off so if the problem persists its not a big job to rectify them. I would have a look into it sooner rather than later as whatever the problem is it could get worse and cause a loss of pressure whilst driving, then you are in trouble.
In the meantime, when the engine is cold, you could either remove the king lead when injector plugs when starting from cold and turn the engine over until the light goes off, or give it 3 or 4 very short bursts of the starter to help pressure builkd before the engine fires.