How to scale and shift a signal with a single opamp?
Do you have a negative voltage available? If so, shift R1 input by -0.5V. This will translate to the output as:

Vout = (inverting input * -R2/R1) + (non-inverting input * (1 + R2/R1) )

Example:

More generally, if you treat your amplifier as a differential you have options to inject voltage on the (+) or (-) side to achieve the offset you want.
More about differential amplifiers here: https://www.electronics-tutorials.ws/opamp/opamp_5.html
This version works on the (+) side so doesn't need any negative voltage.

Notice the inverting gain is adjusted to be 5, for a total non-inverting gain of 6. This is because the input is attenuated by 50% (Why? Look into how a voltage summer works), so we have a net non-inverting gain of 3.
Finally, 0.3333V (1/3 of 1V) is a weird voltage. You can work out a Thevenin equivalent for it using a voltage divider and achieve the same thing (that is, 1/3V in series with 1k.)