When to use indefinite article before "independence"?

Solution 1:

"Independence" is an uncountable noun. When in doubt, I tend to think: Can I count independence as one independence, two independences, three..., etc.? If the answer is "yes", then the noun can take an indefinite article in any situation.

However, as commented by the members, an article can be used "figuratively" to mean a kind of in select contexts.

Your inquiry about independence being a continuously changing state, is thought-provoking. "Independence is a continuously (or continually) changing state" is correct. From childhood to old age, we can see how one's state of independence changes over time. This is a general statement and therefore, "an" cannot be used here.