How Do You Guys Align a Microphone Signal to a DI one?

The delay in the microphone signal is caused by the distance the sound has to cover between the speaker and the mic, so no you can’t let Cubase calculate that as it can’t know where you put the mic.
If you measure the distance between the 2 you can calculate the delay using the speed of sound. In practice it’s probably easier to record something with a sharp attack so you can easily align the two visually.