Hi there, welcome to endless boating forums...
Certain model engines are designed to flow through the thermostats creating a delay to start flowing out the telltale water hole indictor while other models will flow direct/right out the telltale.
As long as the hole isn't clogged up with debris, the rubber impeller is newer and in good strong condition and the thermostats are working properly and their not obstructed with debris from something like old particles of an past/present? broken down rubber impeller or other marine life, all water tubes are clean and clear & aligned up in/from the lower gear case housing/impeller housing on up to the water hose connection points of the engine then the temp delay until warm ought to be normal on your engine....It's been suggested with these designed telltale systems to the thermostats so to help get a better, quicker water flow going outwards for an easier, more confidence feeling that the impeller seems to be operating properly right from the start, would be to drill a small hole in the thermostat flange so it allows a bit of water to get past a cold/closed thermostat until it opens.
Also be sure to keep the end of the telltale water hole clean of bugs, etc. as they can easily get clogged up internally...Either vacuum suck or blow air to the telltale hose to help keep it clean as part of a maintenance schedule/as felt needed
In the following link/conversation there a 3 names to trust CharlieB, Chris1956, j_martin
Just received a used boat (Boston Whaler Outrage) from the mainland. Put muffs on and applied water source, but nothing out the pee hole. We heard that it takes a couple of minutes, but want to make sure as not to seize anything up. Is it true that it either takes a couple of minutes and/or...
forums.iboats.com
Please feel free to post your engine serial number if you'd like some help locating a online parts catalog guide and possibly an OEM service manual part number.