If you launched a satellite into low earth orbit and let it travel indefinitely without course corrections, how long would it take before it hits another object?

Okay, your question is how long until it hits another object also in low earth orbit, AKA space debris.

In low Earth orbit you are not completely above the atmosphere, though it’s pretty thin up there. Most objects we place in orbit don’t need course corrections and likely succumb to the ever so slight air resistance and over time de-orbit and come down in a ball of fire. The same happens for space debris at that altitude.

There’s a lot of debris at various altitudes, but really most satellites that are released into orbit don’t ever have course corrections. The problem isn’t crashing into something, but gradually slowing down and leaving orbit. It’s true the ISS sometimes has to move out of the way of space debris, but that stuff usually passes many football fields away, and the ISS is a big target. A small satellite is like a bullet. Getting hit by a piece of debris going the other direction is like two bullets hitting each other. Doesn’t happen. In fact, in over 50 years of space exploration, it’s only happened a couple of times.