Everything in Time machine runs sequentially at low priority in the background. An initial backup can take all afternoon in the "preparing backup" stage -- but you can continue to use your Mac while it is in any stage of backing up.
If you connect your backup drive again soon, such as every-other day, Time machine can use a System Data Structure called the File System Event Store (a circular list of what folders have changed recently) to compute what needs to be backed up very quickly, and will only take a few minutes in the "preparing backup" stage.
If you leave it much longer, the File System Event Store may become stale, and Time machine will have to re-compute 'what needs to be backed up' from scratch, again taking all afternoon.