You need to get more into opamps to understand what I ment. The opamp returns you the difference between its two inputs, multiplied by gain. One of your inputs is referenced at ground. You want your lowest value to be ground.
So, you need to take from somewhere 0.7v (hint hint resistor network) and reference your signal to this value. So, for example, signal goes to +, reference goes to -.
This way, when your signal will be at 0.7v, the difference between your signal (0.7v) and your reference (0.7v) will be 0, and that's what your opamp will output. From this point, the gain sets the maximum point.