I've been studying Spanish for a while and this concept has still eluded me. I was taught that the structure "creo que..." triggers indicative because the speaker believes it to be true while "no creo que..." is subjunctive because it is not a belief asserted by the speaker. However, in English, we might say "I think..." in two different scenarios with different meanings.
"I think..." could signify me asserting my belief about something such as, "I think the best designer is Gucci," where one could replace, "I think" with "In my opinion" to create a sentence with the same meaning. This example more or less aligns with what I believe the function of the indicative is.
However, we often use "I think..." to indicate our speculation or doubt about a situation. For example, if someone asks "Hey, did Joe leave already" I might respond "I'm not sure, I think so." In this case, I'm expressing doubt by using "I think" in this context. I'm not trying to say "I [definitely] think Joe left" because I'm not sure if he actually did, and I'm not necessarily sure if I'm giving the right information so I want to imbue this statement with doubt, wait...
While writing this I'm realizing that all the examples I've written could be written in another way that is conducive to the formula for using the subjunctive. Rather than translating "I think that..." as in my second example with Joe, it would be better for me to use a structure that starts with "dudo que..." or "es posible que..." to better convey the meaning of uncertainty or doubt that I'm intending to. I suppose the issue I had was that "creo que" always meant to me "I think" or "I believe" when really a better translation would be just "to believe" since "to think" has some ambiguity in its meaning when translated to English.
I know this is post was pretty drawn out and I've already answered my question, but I'll still post it anyway just in case someone more knowledgeable wants to add on or correct something I've said. Or, maybe someone else will find it useful.