That's fine.
And that's perfectly OK as well, but you seem to think it isn't?
I suspect you might be concerned about whether oil has circulated to all the nooks and crannies of the engine in the first few seconds, but really as soon as the oil pressure light goes out it's fine to raise the rpm a bit and put some light load on the engine.
It's actually a good thing to (within reason) raise the rpm very shortly after the OP light has gone out in order to quickly spray some oil up onto the cylinder walls (which will be relatively dry at start up). This is a good thing that the 'cold fast idle' does, but a bad thing is that it tends to not wait for the OP to build up...
Not ideal IMO, but then the 'cold fast idle' speed is probably high enough to spray an adequate quantity of oil around...




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