Are there more appropriate/creative/natural ways this could be translated other than a literal sense?
A literal rendering to me would be like...
痛みは成長の門口です
If you want to play it safe, 人は痛みによって成長する or 痛みは人を成長させる should make sense, although uninteresting. If you want something more literal and figurative, 痛みは成長の入り口 should make enough sense. 門口 is a fairly rare word. You can omit だ/です in a proverb-like catchphrase like this.
EDIT: (Regarding 痛み vs 苦しみ) If "pain" in this context refers to sad life experiences (e.g., heartbreak, failure to pass an audition, someone's death), then I see no reason not to use 痛み. It's at least more literal. 痛み safely refers to both physical pain and psychological pain, and this type of 痛み is essentially a synonym for 悲しみ or つらい経験. See how 痛み is used in lyrics. 苦しみ is also used both in physical and psychological senses, but IMO it tends to refer to longstanding struggle/hardship/suffering rather than one-time sadness. 痛みによって成長した sounds like you experienced something terribly bad, but learned some lesson and became stronger or smarter. 苦しみによって成長した sounds to me like you have been struggling in difficult situations (such as poverty).