To me on my first listen before even having seen the film, I had felt she had gotten a heavy influence from Blake Neely's Supergirl Main Theme, you can hear the exact string rhythm (albeit faster) in the Captain Marvel theme, which I believe is in the second half of the End Credits. The other score I felt like it "wanted" to be was Lockington's Percy 2. There were a few particular moments that had sounded a whole lot like Lockington's theme he wrote for Percy 2. And I agree with the Williamses / Giacchino references, some of the brass riffs / orchestrations sounded exactly like some of the Star Wars action cues of the most recent episodes. In terms of Giacchino, I think she had went the Incredibles route, as some of the cues sounded vaguely familiar from that particular score.
Some of the other Giacchino scores that it reminds me of would be Fallen Kingdom, Jurassic World, and obviously Incredibles 2 as well. Those are all pretty brass-heavy scores, and the orchestration here seems more or less the same. We know how much the Disney execs LOVE Giacchino, so it makes sense they are pretty used to having that sound in almost all of their films. It's pretty much the whole reason he got the Rogue One job.
Honestly to me, the vocal reference doesn't really stick with me much as a Lisa Gerrard reference, as I don't think she was trying to evoke an ethnic sort of vocal-work here. When I heard Waking Up I immediately thought of this track from Percy 2: https://www.youtube.com/watch?v=QVOLZQn1qEk
Another female that sounds a lot like this type of vocal style would be Tori Letzler in Thor 2: The Dark World, which would make a lot of sense considering how that's actually a recurring theme in the MCU, more than you can say for most of them.
04. Why Do You Fight? is in the very beginning of the film when she is fighting Yon-Rogg (Jude Law's character) right? Honestly, for some of the more "synth-heavy" cues I heard more Aquaman than I did Thor: Ragnarok. I would be curious to know if there were actually any additional composers on Captain Marvel, as it would be interesting to see if Andrew Kawczynski had worked on this film as well.
I'm still going to give some time for the score to grow on me overall, nothing specifically had stood out to me in the film besides a few of the brass runs / synth arpeggiations were pretty neat and unique to my ears. I don't know if it was the fact that the score didn't seem to be mixed too loudly for the scenes that had music, but hopefully after a few more listens of the OST I will come to a proper conclusion as to what I think of the score. For me personally, during the post credits scene, the music that I heard playing during that scene was instantly recognizable to me. Not going to spoil anything obviously, but it was the most memorable piece out of the entire film, but that's also because that's one of my favorite scores of recent years, and I have listened to it a lot. I would ramble on more, but I see no point until I begin more familiar with the score.
PS: I'd be quite interested to know what everyone thinks of the "sound"? heard @ about 1:52 in the cue Breaking Free on the OST. I can't really make out what kind of Instrument would actually make that sound, but to me at first it had sounded like a woman screaming something. It almost sounds like straight-up dialogue. Would be curious to know if anyone else had heard that. Also, half-way through this cue reminded me of the "sound" of very high strings that you hear in almost all of Doyle's scores, but most notably the Goblet of Fire. He definitely does something very specific to the strings in his scores that make them sound the way they do, and that is definitely somewhat emulated halfway through this track.