Analog audio delay chips for ms delays have been previously manufactured, based on CCD structures. They have been superseded by digital signal processing since 10 or 20 years. Audio delay in a microsecond order of magnitude can be achieved by a few LC stages.
There may still be video delay line chips around but I haven't used them in a while but they would delay a video line. However, to delay an audio signal by microseconds I would look at tapped analogue delay lines or building a lumped transmission line approximation. Another approach would be an 'all-pass' filter type of delay. You need to define your audio frequency range.
Thanks for elaborating. To implement a constant time delay over a wide frequency range, a linear phase (Bessel prototype) low pass filter is much better suited however.
Group delay can be derived from the filter transfer function, or read from the filter definition for usual filter prototypes, e.g. Bessel filter https://en.wikipedia.org/wiki/Bessel_filter
Filter design software or general electronic simulation tools (e.g. SPICE variants) can calculate it.
For a delay in the amount of microseconds, you would use capacitor values in the range of maybe 1 to 100 nF. It depends on the number of stages you use.
This method works best on a signal which is at unchanging frequency and amplitude.