Yes, it is. Take a look at the SshdSessionFactoryBuilder. It has a number of hooks you can use. Skipping GSSAPI (Kerberos) would be setPreferredAuthentications("publickey,keyboard-interactive,password"). StrictHostKeyChecking can be changed for instance by adding a ServerKeyDatabase via setServerKeyDatabase(). For instance one that always returns true in its accept() method to switch off host key checking altogether. Setting a particular ssh key could be done for instance by switching off handling of ~/.ssh/config (setConfigStoreFactory((h, f, u) -> null)) and defining the key to use via setDefaultIdentities().

Or you could work with a custom ConfigStoreFactory installed via setConfigStoreFactory(), which could return a SshConfigStore that returned a HostEntry with StrictHostKeyChecking=no and IdentityFile=<whatever> and PreferredAuthentications=...

There are really multiple ways to customize this. You may find some of the tests in bundle org.eclipse.jgit.ssh.apache.test interesting, in particular, there are two tests that show how to configure this so that it doesn't use any on-disk files and a pre-defined key.

BTW: depending on what your application does or how it is structured, it may not be necessary to create a new SshSessionFactory in a TransportConfigCallback on each git command. Maybe it is sufficient to just define the SshSessionFactory once and then set it globally via SshSessionFactory.setInstance(). That is what EGit does. Might be possible in your case, too. With a custom ConfigStoreFactory you should be able to configure individual connections as if the config was done in a ~/.ssh/config file, but without actually using such a file, and without having to create new session factories all the time.