That’s going to be pretty tough to do, with decent quality, for $300, unless you DIY.
Parts Express may be your answer.
They sell subwoofer kits, with very high quality woofers, and CNC "flat pack" enclosures. No real wood working skills needed, just some basic gluing, and finishing.
Here is a 12" kit for $218:
https://www.parts-express.com/dayton-audio-12-reference-series-ho-subwoofer-and-cabinet-bundle--300-7092 Then add a plate amp, with adjustable crossover,.like this one for $90:
https://www.parts-express.com/cerwin-vega-v-10s-200-watt-subwoofer-plate-amplifier--299-4046 So for just a bit over $300, you will end up with something that will pretty much stomp all over the sound quality of anything commercially available from a "name brand".
So, unless you want to brag about owning some name brand, don't overlook DIY. Especially if you want better SOUND quality.