Is it possible to restore a macbook pro to an earlier date without an external hard drive backup? I've read that "Time Machine" is the appropriate tool for restoring a Mac to an earlier state.  Time Machine requires the use of some external storage device.

If I remember correctly from Windows, you could revert the state of your computer to a previously set "restore point" -- even without the use of an external storage device.  Does this possibility exist in macOS?
Time Machine doesn't require an external drive but it does require a dedicated partition. Without more info about your system its hard to be more specific. If you have an internal drive with little or nothing on it you can partition that drive and use one of the partitions for Time Machine, given its big enough. Setting partitions will erase the drive.

Why are you avoiding an external drive? I use an external drive for my time machine and it works fine. If its due to the time involved there are workarounds for that.