Blue Origin is admittedly slower than China in developing rocket technology (they haven't even reached orbit yet), but they have a good engine and the New Sheppard has mastered low-velocity vertical takeoff and landing.
Rockets designed in China are blocked from accessing the global launch vehicle market due to satellites containing ITAR restricted components (which is virtually all of them). The reason for this is to curtail China's military acquiring dual-use satellite technology, gaining capital to develop intercontinental ballistic missiles and reducing risk of nefarious actions on the satellites themselves.
China say they'll master first stage re-usability of a medium-lift launch vehicle by 2025. For those of use who want to see an actual space race, let's hope this is a case of "under promise and over-deliver", because that's a Blue Origin level schedule.
The cost of hardware is probably just few percents of the cost of running the space programme itself.
And on top of that, China is the heavy industry supergigant.
Why so, India among other things managed to pull Martian insertion for 1/10th the cost of analogous US mission.
And there is no question, that, at least at the moment, they have both working talent set, and leadership.
There are simple things (relatively speaking) you can slash the cost out of dramatically, where it doesn't translate to a far more advanced and difficult mission, and that includes landing humans on the Moon or Mars safely.
NASA can do cheaper missions. There is nothing particularly special about that for such advanced organizations. NASA spends a lot of money because time (getting a mission right the first time) and scarce human resources are both more important to them than sheer dollar cost in most circumstances, unless we're talking enormous sums of money. They could have attempted James Webb in a much faster timeline at a far cheaper cost, by increasing the risk of failure in the mission; that trade-off is almost always undesirable for NASA.
Simply put, a few hundred million dollars is a very big deal to ISRO, it's not a big deal to NASA. If spending $1 billion on a mission gets you down to 5% risk, or you can spend $100 million at 30% risk of failure, NASA will almost always choose the $1b option because there are not enough human resources to throw at numerous copycat missions and the time cost is immense.