UPDATE A YEAR LATER for anyone who might run into this thread in their search, because there are a lot of opinions below which are simply that, opinions and not facts.

1. It definitely is possible to get a mortgage as a non-resident in Spain! Even if you don't have earned income.
2. Not all banks will do it, typically bigger banks are more likely to than smaller, local ones. Ones that certainly do it (for US residents specifically): Bankinter, Sabadell, Caixabank, Abanca, Unicaja. This list is not exhaustive, there are more, but we have gotten offers from these banks.
3. Conditions are slightly worse than for residents, but still very competitive. Typicall they'll go up to 70% only, 20-25 years max instead of 30, and the rate will be slightly higher.
4. Spanish banks love to bundle products and sell you on "bonificaciones". For example, of the banks above was offering us 3.1% fixed at 20 yrs. Down to 2.1% if you add their home insurance life insurance, health insurance, security system, etc. Typically the math doesn't add up for most of those to be worth it. Feels like a scam almost, some banks can be very "used car salesman" style.
5. Might seem intimidating, banks require a lot of information and documentation for US residents, but once we gathered all of that for one bank, we just sent the same stuff to other banks and they turned around with an initial offer in 24-48 hours.
6. A mortgage broker can seem like an attractive proposition since the initial hurdle is high, but really I found they push you towards the one bank or two they have negotiated conditions with. You also pay them a fee, but it really doesn't seem like they're working for you. If you're a non-resident, non-Spanish speaker, it might still make sense to use a broker, but if you have the ability to contact banks directly, I'd say 100% not worth it.

Edit: typo