White smoke from the exhaust can either be oil burning in small quantities or coolant
burning. Coolant can be readily identified as it is much more dense smoke and it will have a very sweet odor. Oil will be typical thickness and have no odor, and fuel will be the same but will burn your eyes when smelled. Additionally fuel smoke is most often described as black or dark gray but not white.... if you are unsure then a quick smell will tell the story if it is irritating to your eyes.
Given the amount of time sitting, both a coolant burning issue and a oil burning issue are easily possible. Watch your coolant levels over the course of a week and see if they are going down. If they are then it is certain that it is burning coolant. This will be head or head gasket related and is major repair woek to correct involving engine disassembly.
If there is no coolant loss over the week it is most likely oil consumption then and based on the distance driven lately not surprising at all. What happens on these engines is the valve seals that keep oil from running down the valve guide in the chamber will harden from sitting, as they require the oil circulating to stay lubricated.... they have steel valves sliding in and out of them at thousands of strokes a minute, so oil is real important here. If the vehicle sits extended periods these seals dry up and harden, then when the engine is run the valves stroke in and out of them many times dry before the ol circulates to them again. While it is possible to have ring damage cause the same basic symptoms and is caused by the same things (rings dry out then are damaged on a dry start.... the reason they tell you to put a cap of oil in each cylinder on start up after storage), rings are normally pretty high volume smoke and will normally be exhibiting heavy amounts of smoke under acceleration which it doesn't sound like the case here.
The valve seals are major work as well, however they can be done on the vehicle by someone with the right tools and experience. Technically you are supposed to pull the head to change these, however for the sake of time there are ways around that using special tools to hold the valve shut while they are disassembled. Still an expensive job though none the less, both jobs can end up being two days work for an experienced tech, and are priced accordingly.
Check the coolant level to see if it is dropping, and if it is indicating a head gasket issue, have it addressed immediately. If you can not be sure, smell the smoke.... if it is sweet, it is coolant and again address as soon as you can. If it burns your eyes it is fuel and will need to be diagnosed in person to see why it is over fueling. If there is no odor it is oil.... and not an immediate issue, you can drive on it that way without much side effect until you want to repair it.