You're speaking of data latency. It's a great question.
We just launched four satellites. We actually need a critical mass of 12 satellites to be able to detect with the sufficient latency that fits within the specifications of minutes. You're talking about minutes or seconds.
You need more satellites monitoring more often and picking up objects multiple times during their orbital pass to get low covariance, which is the error associated with where objects are in space.
It's a digression of a question, but the exact location of objects in space is a mathematical calculation, so it takes a while to figure that out.