Single supply differential amplifier
Getting the input of a amplifier to work outside its supply voltage range is difficult, but there are possible ways around this:

Is the signal AC?  If so, capacitively couple it to something that floats around &frac12; the supply voltage.

Is the signal floating (not ground-referenced)?  This can be the case when coming directly from some tranducer, for example.  In that case, tie the other end to something around &frac12; the supply voltage.

Shift the voltage level.  This could be done with a resistor divider to the positive supply, for example.  That will also attenuate the signal a little, but that can be made up by increasing the gain a little.  Alternatively, the signal can be shifted by using zener diodes or ordinary diodes forward biased.

Both these schemes will add some offset error.  Everything is a tradeoff.

make a negative supply.  It's not really that hard or expensive, and there are off the shelf chips just for this purpose.  For just powering a opamp, this could be a cpacitive charge pump, which will generally be cheaper than a inductive switcher.

If you already have something that produces a regular clock, a capacitive charge pump can be as easy as a couple of diodes and caps.  I have a few times used the clock output of a microcontroller for this purspose, although then I buffered it with two transistors making a push-pull emitter follower.