Pee availability depends on the plumbing. Pee may come off the thermostat output and if so, you have to wait for the stat to open. On 2 strokers that's 143F engine block water temp. I don't know what stat opening temp is on a 4 stroker but it shouldn't be all that much different. There is more metal in 4 strokers so you have more metal to warm up so yes you could have a delay in a 4 over a 2 if everything is normal.
If plumbed off the exhaust water jacket cover like a lot of engines, or if plumbed directly off the block (follow the hose to see) then you should have water as soon as the water pump has pumped water up to the engine block and filled it enough to get some pressure to squirt. That should be within 30 seconds at idle and normal muff hose outlet pressure.
You could have a dirt dobber's plug in the pee hose.