Time Machine: first backup keeps growing while backing up, never completes

I might have another solution to your problem, as I have finally managed to resolve the issue with my Time Machine.

I have been using Dropbox with Smart Sync, which allows for files to appear on your computer hard drive, although not physically -- the files are actually in the Dropbox cloud. When creating a backup of my whole computer, the Dropbox Smart Sync files seemed to confuse Time Machine, since it wanted to back them up when they are not physically on the computer -- and thus the first backup kept growing and never completed.

In the Time Machine options, I tried excluding the files and folders using Smart Sync and the issue was resolved immediately.