What the best way to get to the rental car facility at SEA if I’m not getting directly off a plane and into a car

I’m coming to Seattle later this year and plan to spend my first night in town, utilizing the rail system before heading further west to ONP the next day and (maybe this is a dumb question) I’m trying to figure out what the best way to get from the hotel back to the airport rental car facility after that first night (yes, I’m gonna use the airport one for a variety of reasons I’ll spare listing here lol).

But I’m wondering, can I just uber directly there and have them drop me off? Or should they drop me off at the actual airport and I take the shuttle bus? Can I even get to the shuttle bus if I’m coming from outside of the airport?

Looking for the most direct and easiest route as it’ll be an early morning start.