When should I consider bigger cards?

My goal is to eventually get into some of the better cards like the Amex Gold, Robinhood Gold, Chase Sapphire, etc.

I’ve been rebuilding my credit since April 2026, when my score was in the low 500s. I had two charge-offs, both of which have now been paid off. Today I am at a 631 credit score.

I currently have two active cards:

Discover: This was close to being charged off, but I was able to save the account, pay off the balance, and get it back into good standing with a $500 limit. I have been positive with payments for the last few months.
Capital One Secured: Opened in May with a $300 limit. I’ve made every payment on time, and Capital One just increased my limit from $300 to $1,800 without me requesting it.

My score has been moving in the right direction, and I’m hoping to reach the low 700s by the end of the year.

I am making six figures now. At what point would you consider applying for something like Amex Gold, RH Gold, or Chase Sapphire? Should I wait until I’m solidly above 700 and have more positive payment history, or is there anything else I should be focusing on first?

Also, any tips for continuing to rebuild and positioning myself for better cards in 2027 would be appreciated.