There is no hard and fast rule as to whether resumes or cover letters are read first. Some employers and hiring managers claim to read the cover letter first (because so many applicants don’t bother to include one), and others say that they read the resume first.
Typically, it would be safe to assume that for positions that require specific skills, experience or qualifications, recruiters and hiring managers would look at the resume first to make sure you have them before taking the time to read your cover letter. This is especially true in fields that require hard skills, such as IT, accounting, architecture, or engineering.
However, it would stand to reason that employers and hiring managers might read your cover letter first to ensure that your writing skills are at the level they require in more creative fields such as journalism, copywriting, and customer service.