How quickly should oil pressure come up?

Any engine takes a few seconds. Of your lifters and making noise for the first 10 seconds you could have various causes, bad lifters, bad oil pump, low oil, clogged oil passages or wrong viscosity.
I live in a 70 degree weather average, 10w30 has worked fine for me.
You could try using a lower grade oil than what you have.
People tend to increase viscosity because shows up a higher pressure, but remember that pressure is basically a measurement of restriction.
There are ways to read if you have the right viscosity between comparing oil temperature vs psi. But will take some testing. And trying to test with almost same starting temperature, use rpms and what not. But its something in my opinion worth doing.
Oil pressure should be close to water temperature, not higher though.
If you use a 20w50 yes it will read a higher pressure but will increase in oil temperature compared to a 10w30.
For cold starts its better a less viscosity oil since it will travel faster. Think about it as honey vs maple syrup.
Using a anti drain back oil filter helps for this cold starts. Since oil pump wont need to fill the filters capacity nor it will drain the oil from the top down, or at least reduce the oil coming all the way down to the oil pan.
Yes cranking no start, can create oil pressure, actually it should. Wont be as fast or a high as operating engine though.
So it does help cranking for a few seconds, not mandatory.