Epistemic status: pretty certain that this is useful for undergrads
In short: When asked what you want to study, say that you're trying to optimize your impact, and keep building up to EA as long as the person seems very interested. Then pitch EA to them.
During my first semester as a student I've found it very useful to use my initial introductory conversation with someone as an opportunity to pitch EA. It mostly goes like this:
Person: What do you want to study?
Me: Not sure, I'm trying to find what to study so I can have as good of an impact as possible.
(with slight variations of vocabulary based on what I know about the person, for instance, with CS majors, I might say something like "I'm trying to optimize my career for positive impact on the world")
After I say this, it seems quite easy to see how eager people are to continue the conversation. They might reply with "That's such an interesting way to think about it!" or "Oh okay". If their level of enthusiasm stays high or grows, pitch an intro fellowship or a reading group to them, or set up a one-on-one meeting!
Pros and cons
This seems like a really low cost to do outreach on new people if you're good at reading enthusiasm levels, because most people will not have jumped through all the hoops that lead to the actual pitch. There's also the fact that you have to introduce yourself anyways, so might as well do it this way.
Of course, this method shouldn't be relied on for outreach. It's just a good way to catch insta-EAs. I suspect more than half the people who could become highly engaged within months would get caught if you tried this on them.
Also, this mostly applies to schools where majors are flexible and are either not picked before starting college, or can be changed after starting without much cost.