"It's remarkably difficult to find those things", she told Journalism.co.uk. "I wind up watching a lot of things and only really enjoying some of them.
"That's fine for me because it's my job as a journalist to understand what's out there. but for people who aren't journalists they shouldn't have to spend hours and hours and hours listening and watching things that aren't great."
And so, following discussions with her colleagues Ben Lillie, co-founder of The Story Collider, which produces science stories in podcast and live event formats, and Bora Zivkovic, blogs editor for the Scientific American, the idea for Science Studio was born.
The platform, which reached its extended Kickstarter crowdfunding goal of $8,000 at the weekend, is now inviting nominations for podcasts and videos about science of up to 20 minutes in length.
Later this year, after consideration by a panel of judges, the winners' content will first be made available to the project's Kickstarter backers - of which there were more than 200 - before being published by the Studio over the course of around a week.
Eveleth told Journalism.co.uk that while there were a number of places where she was able to find key collections of written science journalism, she struggled to find "a good place to find stuff about multimedia".
"I felt like it was easy for me to find really good written content about science. It was really hard for me to find really good multimedia about science. So that's where we want to come in and fill that gap."
She explained that the Studio will be "like an anthology but just on the internet, essentially".
"It's like if you were to publish an anthology of the best of whatever it is, we're doing that but we're just using the internet to do it rather than a book."
She added that by inviting nominations for the content, Science Studio hopes to "harness the power" of the online science community.
"The community of science journalists and science communicators and science lovers online is pretty strong", she said.
"There's a pretty good group of people online who are really interested in science and are on the lookout for these sorts of things and so part of the thing that Science Studio does that's really important to us is that it's not just Bora, Ben and I looking for stuff, it's everybody.
She added that for the content creators, Science Studio will help their work get "time in the spotlight".
"There's so much stuff on the internet, there's thousands and thousands and thousands of podcasts on iTunes that are just classified as science and it's really hard to get your piece or your thing noticed in a lot of ways."
The Kickstarter campaign had originally aimed to raise $5,000 and was going to focus just on podcasts at the start, but after reaching that target ahead of time it increased it to $8,000 to enable it to also include videos.
In time, she added, Science Studio would "like to expand that also to infographics and interactives because I think those are another really important way that people get across a lot of these scientific concepts and these science stories".
"But for now we're doing podcasts and video. Those are our two main areas."
While she said the project took to Kickstarter to help it get off the ground, Eveleth does not want to rely on crowdfunding every year.
"We don't want to have to come back to people every year and ask for money, that's not ideal.
"... We've been thinking a lot about ways in which we could have either a subscription model or do a membership or something like that, so that's something we're thinking about and I'm talking to as many smart people about that as I can, because I think there are a lot of people out there who are trying to figure that exact things out.
"But our plan is to not go back to our community and ask them for more money, I would like to avoid that if possible, in the sense that I would like to avoid crowdfunding campaign.
"If people want the content and they want to pay for it in some way, that's something that we're looking into and maybe that means that people get a subscription and then they get all the stuff either early or they get exclusive access to things or maybe people can pay as a member."
She added that "the power of Kickstarter" at the start is in part helping to "prove that people want the thing that you are making".
"... The answer has been yes which is really nice".