On this, note that while some countries like Australia transfer their Amex credit score, but others don’t. So for any non-Australians reading this - do check, especially if you don’t already have an Amex card and are considering getting one just for this . I don’t remember the details of why it differs, but it does.
I do feel in some ways the need for a credit score as soon as you land is overdone. You can get a secured credit card, you can get a cellphone contract with a refundable deposit etc without a credit score. Normally any such deposits are (a) not onerous (b) repaid in a year. We found it really didn’t take very long to get a decent enough credit score to do anything we needed to do without further hassle. All you really need are a couple of accounts that you pay off regularly. Caveat, we didn’t finance our cars so not sure what extra hoops might be necessary for those who want to do that.