Both @p49p0’s and @DasKairo’s solutions are worth a try! There are two reasons as to why it’s not rendering properly:
You’re most likely at the lowest graphic setting, and that will cause far away objects to not render until you are close enough to the object for rendering.
Z-fighting is a common problem for builds that interlap eachother, but AlwaysOnTop would help solve that problem because it would place the BillboardGui on top of whatever is on the screen. Though, if you’re not wanting the BillboardGui to also be seen through the player, then I recommend trying the first solution first.
If neither of those solutions work, then here’s solution number three: You can reposition the part containing the BillboardGui up a bit, or you can increase the offset by the y-axis using the StudsOffset property by a few studs until you get the desired result!