Since you bank at Chase, I would suggest going in person to see if there is a preapproval for the CSR (or CSP). Also important to note that for the all zero except one scoring boost, the card showing a balance must be a revolving credit account not a charge card (which is not factored). So if you have no balance on the Marriott card, you have 0 of 1 cards reporting a balance. If you did report a balance on it, you would go over the margin of 50% of cards reporting a balance and also have 100% of cards reporting a balance. I actually don't know with only having one revolving card which would benefit you more, but it might be worth letting the Marriott card report a small balance of maybe $5 at statement cut to see what it does to your scores. (Important to note that is for FICO 08 scoring; Amex makes it confusing now because they began giving a VantageScore 3.0 score in addition to the Experian FICO 08 score, and generally the "educational" score is more prominent on their website than the actual score they and most other lenders would actually use.) For AZEO (all zero except one), the biggest gains will come when you have 3 or more revolving credit accounts since you also gain the "fewer than 50% of cards reporting a balance" points. Traditionally, having 0 cards reporting a balance will actually cause a score drop.
@Anonymous thank you for that; it completely changes the conversation. I am not sure on the ITIN/SSN requirements of Citi. Both Premier and Prestige could be viable options for you to cover the remaining travel categories, as well as others that may be missed by not being able to pay with American Express at times. Bank of America has some okay options (much better options with large deposit/investment accounts), but in order to apply with an ITIN I do believe you must apply in person. Discover does ITIN, but acceptance in Europe is going to be lower than Amex, and even in Asia where it should run as a UnionPay card it can be hit and miss at times. I can't speak as to ITIN eligibility, but some credit unions may offer favorable travel-oriented cards on Visa or MasterCard network.
As for the Amex Platinum card, since it a charge card it is scored differently than revolving credit cards. If you are showing that balance monthly on the Marriott card, that should be fine. You are reporting 100% of cards with a balance and more than 50% of cards with a balance since you only have 1 revolving credit card, but it's still likely better than showing a $0 balance in the eyes of FICO and risk management. The reasoning is that you are showing responsible use of revolving credit rather no use of revolving credit.
For the credit history part, the Amex Platinum certainly does count, so if those are the only two things showing on your reports you would have a total credit age of 13 months, with an average age of 8 or 9 months, depending on rounding.