Hi zrei
With a 300 watt amp, a ten inch driver plus the cost of the cabinet build, I really doubt it's possible. IMO, anything within the 500 and under range that gives excellent performance compared to the competition (SVS or BK here in the UK) is really hard to make for less if at all possible.
You may be best placed to scout the classifieds for a pre-owned sub to get the most out of that budget. I stand to be corrected though.