"But it could be incomplete. Say a Dyson sphere still under construction."
Or it's a type of ringworld in sections with tremendous connections between. If you also include Niven's ringworld construction, there could be the inner ring of material that simulates day/ night cycles giving our perception a winking of light.
If we discover Jump drives or, better for our real universe structure, the alterative Warp drive, it will take at optimum 1500 J-1s as well as time refueling or 3000 weeks to reach there. That's about 58 years! Or we wait for a couple thousand years for TL 13 and J4 so it takes 14 years.... Un huh.