So, I'm a little confused on this one. First, I flushed the coolant with the garden hose till' it came out clear. I have replaced my thermostat as well as my coolant temperature sensor. The thermostat had a small gap around it and the new one didn't so I figured I'd replace the coolant temp sensor as it was cheap and easy to replace, still no luck. I pulled the water pump thinking that maybe it had went bad or something and it looked perfectly fine and spun as it should. After all that I still had no luck. So I took my garden hose, removed the thermostat and thoroughly flushed the engine, I put my garden hose into one of the coolant lines and flushed it until it all came clear again. Still no luck! My engine will heat up to about to the first 1/8th of the gage when idling, then it will slowly creep up to about 1/4, of the way up the gage (1/2 way to operating temp.) I haven't ran the engine further than that because I don't want to overheat anything. The strange thing is, once I start to drive, my temperature will lower over the course of a few minutes back down to 1/8 the gage or basically cold. One thing I noticed is that I can turn my water pump if I try to wrench on it decently hard using a screwdriver, but I seriously doubt that it would be enough to cause the issues I'm having.
Does anybody have any ideas?

What year, model, & engine-type?

I'd check the resistance of the sensor. I bought a new one for my 92, when I changed head gaskets. I figured it was easy to change it, since the head was off. Well, as soon as I cranked the engine, within a couple minutes the gauge pegged full HOT. Well I knew it wasn't as hot as it said it was, because I felt all around the engine and it wasn't even warm yet.
I then checked the resistance of the new (made in china) AC Delco sensor. It was way off. I took it out, put the original (made in USA) AC delco back in and sure enough the temperature on the gauge showed cold and then normally went up as the engine warmed. I also used an IR thermometer gun to get readings at points all around on the engine. That confirmed everything was okay.
So, just because it is new doesn't mean it will work, especially if the box says made in china.

If it's your engine not getting up to temp, you might have a bad thermostat. Put in a new one and see what happens. Even new ones can also be bad.