The HDF5 file uses both an abstract data model as well as an abstract storage model. What this means is that how a file is stored on disk may be (and usually is) completely different to how it is represented in your program. It's possible to store exactly the same data in more than one way, and for this not to be apparent to your program.
The HDF5 file format storage specification allows for several timestamps in the data object headers. These are not stored as attributes, and so aren't usually accessible by the high level APIs. It's possible to turn off writing these timestamps using the low level HDF5 APIs, but it's not clear if the relevant features are in h5py. This github issue appears to be exactly what you want, but unfortunately it is still open.