There’s no real evidence for Spanish galleons in Hawaii before Cook, but there are claims that the San Juanillo was wrecked near Maui in 1578 and the Santo Cristo de Burgos was lost off of Kona in 1693 (or 1696).
No evidence, as far as I can tell, exists to positively identify these ships — which are lost Manila galleons — with Hawaii specifically. There’s at least one competing claim for the Santo Cristo; the enigmatic “beeswax wreck” near Nehalem, Oregon. Although that might seem too northerly for a Spanish galleon, the west-east route went from Manila to Cape Mendocino in what is now northern California, then south along the coast to Acapulco. So an off-course galleon might well end up in Oregon as easily as in Hawaii.
There is, apparently, some indirect evidence of contact in Hawaii before Cook, although not necessarily with Spain. For example, there was a Hawaiian word for iron even though there was no indigenous iron making technology and there are stories in Hawaiian oral tradition about visits from non-Polynesians. But they could just as well have been Japanese fishermen blown off course.
There is, from the Spanish side, some evidence that Spanish mapmakers knew about either Hawaii or the Marquesas, perhaps from a voyage by Juan Gaetano.
I don’t know why the San Juanillo is noted as being wrecked “near Maui” or the Santo Christo de Burgos as “off Kona,” but I believe that the source of the claim is Richard Rogers’ book Shipwrecks of Hawai’i.
There are at least two historical references that say the San Juanillo was wrecked on an outward voyage from Manila in 1578 in the San Bernardino Strait near Samar in the east of the Philippines. As for the Santo Cristo de Burgos that loss is anybody’s guess as she and all on board just vanished. She is a strong contender for the Beeswax wrecksite in Oregon, and I have never come across the reference to Kona, if correct it was in 1693 . Tom@Shipwrecks-Philippines.com
There is at least one large piece of direct evidence for pre-cook contact in Hawaii. In the above referenced book “shipwrecks of Hawaii” it is mentioned that the bishop museum has artifacts from a burial in waipio valley that is dated from the late fifteen hundreds. Included in the burial is a sizable piece of flax seed sail cloth and the remains of an iron dagger or sword. Neither of these objects could have originated in Hawaii, and based on the date the Spanish indeed would seem the most likely candidates for their origin. I have personally confirmed that the museum does in fact have these artifacts.
In 2012 I gave a reply saying there was evidence of the San Juanillo being lost in the San Bernardino Strait on leaving the Philippines. All the contemporary reports do not seem to confirm this and now some four years later I am beginning to think that Rick Rogers may be correct in thinking that the San Juanillo, one of the five missing Manila Galleons is lost off Maui. Japanese swords were carried on Manila Galleons at the time and even early Spanish swords were of the exhaliber type, also the white bust carving at the Bishop Museum is strikingly similar to a Spanish or Dutch captain.
http://www.shipwrecksforwalkers.co.uk
Richard Rogers, in this article in The Honolulu Advertiser from 2003, mentions the Kona theory.