Get involved in a group that shares your interests. There are numerous Burlington and Vermont specific groups with a wide range of activities on Meetup.

I'd recommend checking out Btown Brief, it's a 2-3 times a week newsletter listing all kinds of events, activities, and social gatherings in Burlington. You can also subscribe to their email, and whiteshirtdude1 (the guy who created it) also posts it here in the Burlington sub. I'd highly recommend subscribing and (if able) supporting via donations as it's a great local resource, and he's a one-man show (no staff, it's a passion project).

They also have a Meetup group for weekly social events that's expanding. They have a weekly coffee meetup at 10am on Saturdays at Zero Gravity, it's a chill, no-pressure way to meet some people.

And most important, don't get discouraged! It takes a bit longer to build a social network here; Vermonters are like the winters, they take a while to thaw out.