Time machine backed up size keeps increasing

This is the first Time Machine backup I've done after factory resetting laptop (Macbook pro 2019 Catalina 10.15.6).

The backup started off displaying a sensible amount of backup to run (e.g., "backing up 0 MB of 20 GB"). Then after hitting or getting close to that total, the backup size increased, i.e: Backing up 22.00 GB... Backing up 25.00 GB... and continues like this infinitely.

How can I solve this issue?

There are some details missing from your question, but here's my guess based on what you've said:

The "factory reset" probably looks like a first-time backup to Time Machine, and so it is backing up your entire HD/SSD. If you back up tomorrow, the amount of data will probably be much less.

In other words - this may not be an issue at all - simply Time Machine doing what it was programmed to do.