Using the path of practice (the Fourth Noble Truth), we can learn to pay attention moment to moment, developing insight and concentration. Each moment of mindfulness is another moment of freedom from suffering, and in that freedom, indeed, peace is possible.
Compassion is classically described as the quivering or trembling of the heart in response to suffering. Our habituated responses may be to deny or repress our suffering. As we learn to open to suffering with a balanced mind, we discover the natural responsiveness of the heart which brings us into a relationship of care and concern for the world we live in.