The "primaryness" of a source emerges in relation to the researcher's engagement with it. The UC Berkeley Libraries define primary sources as "either created during the time period being studied or...created at a later date by a participant in the events being studied (as in the case of memoirs)."
(source: Finding Historical Primary Sources: Getting Started, last updated 8/12/18, http://guides.lib.berkeley.edu/c.php?g=4409&p=15606)
When determining primary sources for your research, it's helpful to give yourself a historical context that defines your search. This could be a range of dates. It could also be determined by geographical sites of origin. It could further be specified by the kind of creator(s) or audience(s) you are interested in. You might also be interested in a specific type of source in terms of genre or format. Some examples include:
Databases and digital repositories can offer a multitude of paths to potential primary source material for your research. In addition, try searches for published works in CLIO, limited by date of publication. Finally, see below for tips on researching in archives and special collections.
According to the Barnard Archives Research Guide Archival Research at Barnard and Beyond, which I recommend for its resources and strong conceptual foundations for archival research, "Archives and archival collections are unique constellations of unpublished records made in the course of normal activities. Archives are comprised of primary sources, but not all primary sources are archival."
When doing research that involves primary sources, you might be interested in visiting an archival collection.
To explore what's available in archival collections at Barnard and Columbia, you can start with a CLIO Archives search. Use keywords that might map onto areas that interest you (including names of possible creators of records, subjects/themes, places).
Archive Grid lets you keyword search collection descriptions from archives around the world. Entries provide contact information and links to relevant web sites. You can narrow your search to archives in the New York City area.
Archivistas en Espanglish is a collective of transnational Latin American & Latinx archivists and cultural workers that aims to incubate and amplify spaces of memory-building within las Américas. From their website: "we center the lived and intersectional histories and experiences of nuestros pueblos & communities as they exist: past, present & future." AE's web site has an abundance of amazing resources related to Latin American and Latinx archives and memory work (in particular, look at the Recursos section!)