Restore Mavericks from Time Machine
Time machine can't hold backups of the operating system. It only backsup your personal files. The steps below will allow you to downgrade.

macOS will not allow you to run an older installer so you will need to circumvent it by doing it from a bootable drive.

You may also consider running multiple versions of OS X. You can do this by partitioning Macintosh HD. It doesn't require a format so your files are safe. Do the same steps below except first partition the hard drive before restart. In the installer, select the other partition.

Requirements:


8GB flash drive;
that you had an apple ID when you had Mavericks installed.


How to do it:


launch the app store;
go to purchases and look for Mavericks;
download Mavericks and close the installer when it opens;
plug in your flash drive;
format the flash drive as Mac OS extended (journaled);
create a partition with a GUID scheme;
launch terminal and run this command:

sudo /Applications/Install\ OS\ X\ El Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled --applicationpath /Applications/Install\ OS\ X\ El Capitan.app --nointeraction
hit enter and type your password;
wait for the files to copy - this will take a while;
restart your Mac while holding option and select your flash drive with the arrow keys and hit return;
proceed through the installer normally.


This shows how to downgrade to El Capitan. The process is the same for Mavericks.
http://www.macworld.co.uk/how-to/mac-software/how-downgrade-from-macos-sierra-el-capitan-remove-macos-sierra-3581872/

Let me know what happens.  I hope this is helpful.

PS: backup any files you want to save from the flash drive because it will be erased.