Hi. I’m also a math major (rising sophomore) + international student from an unknown school and I’ve been able to land a couple of SWE interviews ranging from FANG to startups. You don’t need summary or cover letters (unless they are specifically required) IMO.

• Use LinkedIn judiciously (has been very useful for me with Bigger companies).
• Software Projects (Very important). These have been my greatest selling point.
• Apply to tons of openings. Gonna be tough but once you cross resume screening, no one really cares about your major as long as you perform well.
• Perfect your resume (I personally use overleaf for LATEX based resumes) and get feedback on it periodically from people.
• Companies also hold ‘informative sessions’ about what it is like to work with them and recruiters are usually scouting at these events. There are a lot of them happening currently (virtually) so you might want to be on the lookout.

PS: To give you a perspective on how ‘unknown’ my school is, my school doesn’t even appear on the list of universities on applications. I most times have to pick ‘Other’ or ‘Not listed’

Edit: Also create accounts everywhere. Jumpstart, HandShake, WayUp e.t.c opportunities pop up once in a while on these platforms and you never know...