How to read the datasheet of an ultrasonic sensor?
A big problem with minimum range is that these transducers have significant Q, as demonstrated by the bandwidth of 1-2 kHz. This means that the transmitter pulse rises and decays slowly. And the receiver pulse rises and decays slowly.

Edit:
The slow response of the envelope means that a reflected short-range pulse enters the receiver before the transmitter has entirely decayed. The transmitter inevitably sends a direct signal to an adjacent receiver, and the much smaller reflected pulse may be hidden by the larger direct-path signal. The 2cm minimum range for HC-SR04 is optimistic, especially for small irregular reflecting objects. To improve the minimum range, rise and decay times should be shortened.

A simulation of a similar bare 40 kHz transducer yielded a slow envelope rise (top diagram).

 The transducer bandwidth can be broadened by resonating out the large parallel transducer capacitance of the piezo element (C3):







simulate this circuit &ndash; Schematic created using CircuitLab
 For example, a transmitter circuit (partial) could look like this, with the pulse source lasting about 150 microseconds. The transmitted amplitude should die away as quickly as it rises on its leading edge:







simulate this circuit