This fits your budget and comes with a freewheel. If you want a steel bike I would go with the Kilo TT, other than that for that price range the next best thing is used bikes. Which I wouldn't recommend if you don't really know what you're looking for in the first place. They only have 1 huge size left on that site, but you can probably find it on another site. Only thing you would need to do is add a back brake.
https://www.citygrounds.com/products/aventon-cordoba-track-bike-2019?gclid=CjwKCAjwvJvpBRAtEiwAjLuRPZdzH0CXIhUeo0l2FxfObPgEmERacrOHN_Az3kWtSlRlO6Z7My16PxoCM1gQAvD_B wE&variant=19268810768495