Is there any parking near by ?

There are no parking unfortunately

Nisa is correct. The SoDo station does not have a parking lot. Tukwila and Angle Lake stations are the only two with parking. Parking between 1st Ave, Airport Way, and Lander is very limited. Street parking for 2+ hours is usually taken by 7:30am on week days.

One stop down( north), at Stadium station there is a parking garage

For LR commuters, there isn't reliable parking. There is a lot for Postal Service workers and vehicles, and the rest is street parking. I might be mossong something since I'm considering a block/2 block area however.