It will be burnt up by the time it runs out of fuel, though.
For a good one it has to be hydro-formed out of seamless pipe, which is likely hot-stretched (like wire drawing, but using an induction heating coil in place of the die, and independently controlling the feed-rate and the pull-rate) in advance to retain consistent wall thickness in the engine despite being cross-section after hydro-forming. Also probably incremental hydro-forming with grain-structure-fixing re-heating between stages.
The hard part is just that most of the work is in making the hydro-forming dies/tools, not then using them to cheaply produce more engines.
Of course, you can definitely make a BALLISTIC missile with a couple hundred mile range using a solid rocket engine, and probably for fairly cheap (especially if you don't particularly care about accuracy)
Also: Scud missiles are comparable, made outside western cost inflation, and still ~$1M each. So I'm guessing you can't get a ballistic missile anywhere near $10k (at least, not one that isn't more likely to kill its owner).
https://disclose.ngo/en/article/war-in-ukraine-how-france-de...
(An order of magnitude larger helicarrier contract was cancelled eventually.)