Git operations fail when using SSH with private key because user input is required to continue

When a repository is set to use an SSH remote URL, and the authentication is done using a private key, the push process, for example, hangs with this output:

git -c diff.mnemonicprefix=false -c core.quotepath=false commit -q -F D:\Temp\s5arqixk.lhh

git -c diff.mnemonicprefix=false -c core.quotepath=false push -v --tags --set-upstream origin master:master
Pushing to git@github.com:<ommitted>.git

The server's host key is not cached in the registry. You
have no guarantee that the server is the computer you

think it is.
The server's rsa2 key fingerprint is:
ssh-rsa 2048 ab:<ommitted>:9d

If you trust this host, enter "y" to add the key to
PuTTY's cache and carry on connecting.

If you want to carry on connecting just once, without
adding the key to the cache, enter "n".

If you do not trust this host, press Return to abandon the

connection.

As this message states, I would need to press y to continue, but I can't. The only way I can push the changes to my repository is through the Terminal, which accepts the command git push and does what it should without any issues.