if you have a reproducible build, then the notion of "software was built on date by user" is kind of useless information, no? Because it does not matter - if you can verify that a specific git hash of a codebase results in a particular binary through reproducible builds, a malicious adversary could have built it yesterday and given it to me and i can be almost surely confident (barring hash-collisions...) it's identical to a known trusted team member building it.

Having information about which git has was used, as well as the time it was published, is part of the source distribution so an output can contain references to these inputs and still be deterministic w.r.t. those inputs.

If you REALLY want to know when/who built something, you could add in an auxiliary source file which contains that information, which is required to build. Which is essentially what compilers which leverage current time do anyway, it's just implicit.