It really is simple ... God created the stars on day 4 ... and the text says He created them to be used to mark days and seasons (my paraphrase) ...
If we couldn't see the light from those stars (because as you say, they are too far away) ... how could we use them to mark the seasons?
The obvious answer is that He also made the stream of photons from there to here so we could see the star.
A more interesting possibility is that God created the universe from material nearby the solar system, via a “white hole” phenomena. A “white hole” is predicted by Einstein’s General Relativity equations. It would have been a one-time event and would have relativistic effects in that it would move far, far faster than light. As the event horizon of this white hole passed us, we would continue to be able to see it even though billions of years would’ve elapsed in space. Yet only 6000 years would’ve elapsed here on earth.
Interestingly, the Bible at least implies just such an event has occurred:
Psa 104:2 Who coverest thyself with light as with a garment: who stretchest out the heavens like a curtain:
Isa 40:22 It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth them out as a tent to dwell in:
Both passages speak of God stretching out the heavens like a curtain. That’s how such relativistic effects would’ve appeared from the earth. The stars would’ve moved with incredible speeds, like the stretching forth of a curtain.
Anyway that’s how light from billions of light years away could’ve reached us, when only 6000 years have elapsed on earth.