Blowing smoke right after start up is often just burning condensation out of the system… Very noticeable living in a high humidity area. The only way to 'escape' this is by parking in a climate controlled garage.
Sorry for the pun
But also why they always recommend running a vehicle for enough time to get up to normal op temperature. It's like 15 minutes minimum
If you have a bad head/gasket, and trace amounts of coolant are leaking into your cylinders, this could be verified with a cylinder compression check. But usually you have to overheat the engine or something To have caused this