So, how do justice, tranquility, common defense, general welfare, and the blessings of liberty achieve "a more perfect union?"
Well, maybe some people think a better union of states 'contains such.
People often like justice, peace, ability to defend themselves, public safety, and liberty.
General welfare for instance,
"After the Great Fire of London of 1666, it was realised how much the traditional construction of buildings had aided the spread of the fire, with the close proximity of buildings and the incendiary nature of building material such as timber and thatch fuelling the fire.[3] Several acts of Parliament over the next century attempted to improve building regulations"
https://en.wikipedia.org/wiki/Building_Act_1774
The laws of a society can make it better or worse.
Though better and worse is subjective.
People more willing to be part of a Union if there is Justice and fairness, less cause for war when rules are fair and just.