I can fill the viewfinder of my camera by zooming in on a stop sign a mile away too, but that doesn't tell me its size, or its distance.
But it does. Should be relatively easy mathematics, and depends on the magnification factor of your lens and the distance you would be able to fill the STOP sign from when using the shortest focal length of the lens.
Say if you can fill the viewfinder at 2 meters with a 75-300mm lens at 75mm, you should be able to multiply the distance with the zoom factor, which in that case would be 4.
So here's a real-life example, I took two photos of a smallish painting (sized 33cm × 20cm) in my flat, filling the viewfinder at 300mm and 75mm, and it checks out. At 300mm I was 5 meters away, and when shooting at 75mm, the distance was only 1.20m.
For copyright reasons I can't post the photos of the paintings, but you can actually try it out yourself. Calculate the zoom factor of your lens by dividing the longest focal length with the shortest of your lens, then apply that when shooting the stop sign. In my case, if the mile-away STOP sign filled out the viewfinder, I would just divide the distance by 4, and find out I should walk three quarters of a mile closer to fill the viewfinder at 75mm.
Oh, and also that the STOP sign is really huge.
Edit: If you want to know the actual size of the STOP sign, you can do that too. Shoot something that you know the size of, by filling the viewfinder, then apply those measurements and the distance you shot it in, to calculate the size of the STOP sign.