I haven't actually tested the following code, but this is kinda what I was thinking:

    private void FastForward(Commit fastForwardCommit)
    {
        var checkoutOpts = new CheckoutOptions
        {
            CheckoutModifiers = CheckoutModifiers.None,
        };
            
        CheckoutTree(fastForwardCommit.Tree, null, checkoutOpts);

         // TODO: Update Reflog...
    }