It makes more sense to have the parts in increasing or decreasing importance. For example, in the case of filenames, they sort better if you have year first.Why? Isn’t it basically arbitrary?
So: YYYY-MM-DD-HH:MM:SS.dddd
The US military uses (or used) the unambiguous format: 4 Jul 1776, or 4 Jul 76 and that's how I give my birthday when asked. No one has had a problem understanding what I mean.
The standard American format is broken and stupid, but it won't seem that way to most Americans because it is what they're used to.