Absolutely. A company can apply for a permit. There's a cost associated with this, so they usually do it with an intent to proceed, but it is a while before they get to building.
In that time, a lot of things can happen. Their construction costs can go up. The interest rates can go up. They may face some local opposition. There may be different issues that cause them not to get to the point of a housing start.
A permit is an indicator. It's not perfectly correlated with a housing start, because ultimately, some things may get derailed before they get to a housing start.