I am legally obliged to waste 2 years of my life, when is the best time to do it?

I'm 17M and looking to major in maths and maybe go into finance. There's a decent chance I'll go to university in the UK or the US and not my home country.

The issue is, I'm from a country that requires mandatory military service (about 18-21 months), but its flexible I can choose to go anytime before I'm 26.

Option 1: Go right after I graduate high school. This gives me a 2nd chance at uni admissions and I can apply to some reaches. But it also means I'm 2 years older than everyone in uni, and from what I hear, this might hinder me socially.

Option 2: Go after undergrad. With this, I can actually enjoy uni (some of my friends are applying for the same unis as me too), but the issue is that I'll have a massive gap in my resume that says "I stood at a nuclear-armed border with a rifle for 1.5yrs, this doesn't have anything to do with maths, but pls hire me, oh and also I got paid less than minimum wage while doing it"

Option 3: After masters?? idk but i feel like this is gonna look worse to employers

How much will it hinder my ability to do social things in uni if I'm 2 years older than everyone (option 1)?

How bad will the 2 yr gap in my resume look (option 2)?

ANY advice is welcome!

tl;dr: being 2 yrs older than everyone at uni VS 2 year gap in resume that says "stood at some border"