Can I buy games off of the PS Store without being on the console?

Yes, as long as you have a Playstation Network account, you can purchase things online or through the Playstation mobile app.

From the app:

Once you get your PS4, just log into your account and go to your Purchased section of your Library (far right on the main menu) and Battlefield 1 should be there and available for download.

Another useful thing is that once you have a PS4 set up, you can remotely tell it to install games you've purchased from the app. It helps for those times your coworker convinces you to buy a game at work and you want to play as soon as you get home.