@theunis, you can use Revolut. AFAIK, you don’t need to show proof of address, you just need an EU address to receive your physical card (costs 12€).
They just recently launched personal IBAN’s so it can act as a full account.
Other than that, you can try speaking/chatting with Activobank here in Portugal (they have online chat I think) if they are willing to open an account for a non-resident. They are IMO the best portuguese bank, no fees, free SEPA transfers, everything can be made online (great app and website).
They allow an international phone number for SMS verification. But if you use the mobile APP they skip it, I always use it even when I’m on the desktop.
Best part, you get your debit card and PIN code right on the spot when you open an account, so if you can get a bill or statement with your name and a portuguese address, you’re good to go. They might ask if you work or for an income statement, tell them you’re not employed and just moved to Portugal, they skip it.
Credit card I’m not sure but I think they send it to the address, but the limit is so low that it isn’t worth it.
Bonus points, this debit card can be used to charge the Revolut account as long as you have 3D Security enabled (only asks on the first use).
I’ve successfully charged my Revolut with 15k EUR in a single transaction from the debit card, then wired it via Revolut to my supplier in Hong-Kong. Cost? 0€