An engineering degree
is a kind of experience, and a particularly valuable one at that.
If FIRST says they want someone with the experience of a 4-year engineering program, that's up to them. The job posting also says they desire 1-5 years of industry experience, and that excludes a whole lot of other people (such as myself). If you take a gander at the technical job postings at
jobs.google.com and
jobs.apple.com, you'll see that the majority say things like "BS in Computer Science or equivalent experience". Some say, "BS/MS is required". And a few say stuff like "PhD + 3 years of industry required". In my random clicking through a couple dozen postings, I only found one that said, "Strong computer science fundamentals required - no matter how you got them."
That said, it's quite possible that FIRST would consider strong applicants who demonstrate that they have experience equivalent to an engineering degree. Why not submit your resume and find out?