Looking at the time when Beast is first confronted by Riku about his sudden appearance in Hollow Bastion. In the English script (I'll just post it here for easy reference):
Beast: "I simply believed. Nothing more to it. When our world fell into darkness, Belle was taken from me. I vowed I would find her again no matter what the cost. I believed I would find her. So, here I am. She must be here. I will have her back!"
Thematically I think him saying he "believed" plays up with what was literally just happening in Neverland (and briefly in Traverse Town before the flashback with Kairi's grandmother) where Sora was basically shown how powerful "believing" can be. I think Beast restating that his "belief" was what got him to Hollow Bastion was, most likely initially, just a literary repetition to solidify the concept of the power of believing which eventually morphed into the whole "heart is a guiding key" thing. (While it is entirely possible that they are planning/decided to retcon in some sort of waking explanation that goes in addition to the initial "lets just emphasize the believing thing", I am fairly sure this is what the scene initially was supposed to represent).
However... because I am a complete nerd I just wanted to point out something I noticed in the Japanese script of this scene...
(for those interested in the original text):
ビースト:「私は信じた ただそれだけだ。私たちの世界が闇にのまれた あの時――さらわれたベルのもとへ 私も行くと誓った。そして私はここにいる ここに必ずベルがいると 信じている。ベルを返してもらうぞ!」
What I noticed (that any of you who know Japanese may have already spotted) is this line in particular: ベルのもとへ 私も行くと誓った。/ I vowed I would find her again
This might be a huge coincidence but he uses the verb 誓う (chikau), nominally chikai. Chikai being, obviously, the Japanese title for 3s theme song. It made me smile at the thought that there is a slight connection. While this (tentative) connection only really works in Japanese, it's almost uncannily evocative of the ending of the third game in that Sora is literally doing the same thing in order to bring Kairi back like...right as Chikai plays, even. Chasing her heart through the dark because he promised he would.
Goosebumps, man.
But...this probably just a coincidence.
Do I think that Nomura considered Beast's soliloquy when he planned KH3's ending? Not likely. But it's a fun connection nonetheless.
...or at least I think so ._.'