Here's a structured list of Spanish-founded colonial institutions of higher learning in the Americas (and other colonies) that were open in principle to Indigenous students, along with the caveat that in practice admission of natives was limited and mostly channeled through special "colegios de indios."

🎓 Major colonial universities (Royal and Pontifical)

The Spanish founded roughly 30+ degree-granting universities in the Americas before independence; the main ones ( Wikipedia: List of colonial universities in Hispanic America):

Details on several of these: San Francisco Xavier de Chuquisaca ( Wikipedia), University of Mexico ( Wikipedia), Córdoba, Javeriana and Bogotá ( Hispanic Outlook,  Catholic Encyclopedia).

🏫 Institutions founded specifically for Indigenous students

These are the clearest answer to "could be attended by natives" ( Hispanic Outlook,  Wikipedia list):

• Colegio de San José de los Naturales (1527, Mexico City) — Franciscan school for the Indigenous, one of the first in the Americas.
• Colegio de San Juan de Letrán (1548, Mexico City) — founded explicitly for mestizo and Indigenous orphans.
• Colegio de Santa Cruz de Tlatelolco (1536, Mexico City) — the famous Colegio Imperial de Santa Cruz, the first higher-education institution for the Indigenous nobility (Nahua); its graduates, like Fernando Alvarado Tezozómoc and Hernando de Alvarado Tezozómoc, became chroniclers.
• Colegio de San Andrés (1580s, Mexico City) — Jesuit college for Indigenous students.
• Colegio del Monte / colegios in Cusco tied to San Ignacio, which admitted sons of Inca nobility.
• Colegio de San Francisco de Borja (Lima, 1614) — for sons of Indigenous caciques (later also open to Spanish creoles).

🌏 Other colonial possessions

• University of Santo Tomás (1611, Manila, Philippines) — the oldest Spanish-founded university still operating in Asia, open to Filipino (Indio and Chinese mestizo) students.
• In the Marianas (Guam) and the rest of the Spanish East Indies, only mission schools existed, no university.

Important caveats

• Formal admissions barred most casta students, but exceptions existed: San Marcos in Lima admitted Indigenous nobility, and San Ignacio of Cusco deliberately recruited Inca nobles; the Crown ordered caciques' sons educated in colegios such as San Francisco de Borja in Lima ( Wikipedia list).
• Many "universities" operated out of Dominican/Jesuit/Augustinian convents, so the line between college and university is fuzzy — some colegios (e.g., Tlatelolco) taught advanced Latin, rhetoric and philosophy, effectively at university level, without granting degrees.

If you'd like, I can turn this into a sortable table or timeline (e.g., a Marp/slide or table canvas), or expand the list to all ~30 minor universities.

Here's the British counterpart to the Spanish list. The key contrast: Britain founded far fewer degree-granting institutions in its colonies, and institutions specifically for Indigenous peoples were rare, small, and often short-lived — though nominally "open," most were effectively for settlers.

🎓 The colonial colleges of British North America (1636–1769)

The nine degree-granting institutions chartered in the Thirteen Colonies ( Wikipedia: Colonial colleges):

• Dartmouth's charter explicitly included the education of Native American youth ("and also of English youth and any others").
• Harvard built an "Indian College" (1655) which graduated a small number of Native students, most famously Caleb Cheeshahteaumuck (Wampanoag, class of 1665).
• William & Mary ran the Brafferton Indian School (1723–1770s), endowed by the Boyle bequest for "the maintenance and education" of Native boys.
• Dartmouth grew out of Moor's Indian Charity School (1754, Lebanon, Connecticut), founded by Eleazar Wheelock; his student Samson Occom (Mohegan) became the first Native American to publish writings in English.

In practice, only a handful of Indigenous students ever graduated from these colleges.

🍁 British Canada (pre-1867)

• King's College, Windsor, Nova Scotia (founded 1789; now University of King's College) — the oldest chartered university in Canada, though originally Anglican and effectively settler-only.
• McGill University (chartered 1813, opened 1828, Montreal) — colonial-era founding.
• King's College, York (Toronto, 1827; now University of Toronto).

🌏 British India

Britain founded no universities in its first two centuries of rule; the first three came only after the 1854 Wood's Despatch, modeled on London University ( Firstpost):

• University of Calcutta (1857) — oldest multidisciplinary university in the subcontinent, explicitly open to Indian students.
• University of Bombay (1857) and University of Madras (1857).
• Earlier, Hindu College, Calcutta (1817; later Presidency College/University) — founded by Indian reformers with British support ( Times of India), plus missionary colleges like Serampore College (1818).

🌍 Other colonial possessions

• Cape of Good Hope: South African College (1829, now UCT) and Stellenbosch Gymnasium (1866, now Stellenbosch) — Dutch-descended and British settler oriented.
• Ceylon: Ceylon Medical College (1870) / University College (Colombo, 1921) — the island got no full university until 1942.
• Caribbean: no university until Codrington College, Barbados (chartered 1830 as a college, affiliated to Durham) — mostly for white planters' sons; University of the West Indies came only in 1948.
• Hong Kong: none until the colonial government's University of Hong Kong (1911), open to Chinese students.
• Australia/New Zealand: the Australian College (1831) and the University of Sydney (1850) and University of Melbourne (1853) — early Victorian-era foundations open to settlers and (later) Indigenous students.

Key differences from the Spanish pattern

• Spanish America got ~30 universities starting in 1538; the British in the Americas built only 9 colleges in 150 years, all for creole/settler elites ( Wikipedia,  Hispanic America list for comparison).
• The Spanish ran dedicated institutions for Indigenous nobility (Tlatelolco, San José de los Naturales); the British equivalents (Brafferton, Moor's School, Harvard's Indian College) were small, underfunded, and died out within decades.
• In most non-settler colonies (India, Africa, Caribbean), Britain's policy was to avoid founding universities until the mid-19th century, relying on missionary schools and sending elites to British universities instead — the Spanish founded universities in their colonies two centuries earlier than the British did in theirs ( Firstpost).