Associates degrees are non-existent and not recognized in the EU, and most if not all countries require you to be a graduate to be eligible for hire, which would make a student visa the easiest route.
Luckily many countries offer tuition completely for free; though bachelor degrees are often taught in the native language. If your Spanish is solid, you could of course go to Spain, else with English you'd be somewhat restricted to Ireland and Malta (English is the second official language, but the primary for tuition).
Other than that, some universities have English taught bachelor degrees, so you'd have to research them individually. Finland is very English- and Tech-friendly, for starters.
Some countries consider limitless ancestral pathways, but you must have factual evidence (birth records, marriage certificate etc.) that are unquestionable. Several countries also consider the paternal side only, meaning you must be able to trace your lineage through your father's male family line only.
I haven't heard of anyone being able to trace their line back to the discovery of America, but who knows. Certainly heard of some Brazilian successfully claiming German citizenship dating back to refugees from WW1, which is already 110 years ago and 3-4 generations later.