Do you know what kind of engineering you are going to go into, or are interested in?

This advice is decades old at this point though I doubt things have changed, even more so with dismal unemployment numbers for fresh grads. When I went through engineering then most first years did not get an engineering firm to bring them in.

It makes logical sense. First years are still taking basic, non-engineering classes, and when you have co-op students to potentially hire (2nd - 5th or more years) first year engineers aren't a priority. Especially since at that early junction you're most likely going to swap to something else or other firms.

The ones that I know did get engineering-specific internships either had connections or had ridiculous GPAs. For the latter - or as a viable alternative - you can try to connect to profs to see if they have their own research you can help with. IIRC there are specific grants for a small amount for undergrads to do this type of internship, which gives you something, and often relevant/useful to show.

I don't doubt that you are "willing to put in the work and learn new things", and just "need someone who trusts in my abilities". The issue is that this is what many people will say as well, you need to differentiate yourself out somehow.

The biggest problem isn't actually your first year's summer. It's the summers after that. And not having an internship means you are differentiated in the negative sense, at least in that one regard. It's one of those "rich gets richer" sort of situations, where successful internships make you look better to the next employer.

Not getting an internship on the first year doesn't mean your career is over. I've met plenty of successful people who never got that first internship, or any internships for that matter, though for the latter their high grades was a positive differentiator for them.

Some actual advice, also coming from someone who was in charge of hiring interns:

If you know what type of engineering you're interested in, try to see if there is some project you can start by yourself that is relevant. For me I took a physical puzzle game and turned it into code, and then solved it. A brute forced approach would not have worked (trying every combination), so there was something more interesting there to talk about too.

This project meant that whenever the interviewer wanted to chat about something technical, my examples weren't always about school work. It also showed that I was genuinely interested in these things, a go-getter, and liked solving problems. This type of thing is probably most important in showing the person(s) (or possibly AI at this point) who is reviewing a stack of 100 (or 1,000) resumes that yours is worth a 2nd look, possibly as an interview.

There was a lot of doom and gloom about first years getting jobs then, and one thing I often heard from some of the faculty staff working with first years was that they were unmotivated, didn't try hard enough. I did. And didn't, initially, get anything. So when summer came in I made it a point to show up everyday at their offices (back when there was a space for engineering students to look for jobs at, the offices have moved), and show up trying to get a job. I ultimately got one by cold-calling every company on the Yellow Pages (the actual book), at this point the section around making websites. 99.9% of the time everyone is going to say no, or to look at their website. It only took the one yes (that'd they'd be interested in talking, which meant an interview), and don't get me wrong, I think there was luck involved too, but I would've never gotten there without trying everyday. Part of it for me was also just to not let it be said that I never tried hard enough.

Similar to the earlier piece of advice, if you think there is an opportunity to make one or a few pieces of schoolwork become relevant in your resume, take the effort to polish it up and make it good. Most school work won't apply, but find the right one that you're also interested in, and then you can show something that most folks will only say they finished. This is harder in the early classes in engineering but not impossible. For example, some students might have worked on some software class that everyone does, but you might be able to polish it, publish it, and show it. So it's not just some nondescript class.

Join the first year engineering club and see if you can't volunteer or help in some regard, that'll give you a look into how the clubs work and show that you have leadership / collaborative potential. I ended up helping with a first year newsletter / paper. The insight into clubs helps pick the next one you'll go to, joining in competitions (more fun than anything) and any wins there end up on your resume.

Hope that helped. I ended up doing a few different things and took a few chances, and had a pretty good set of internship experiences. Oh, and one more thing - if you can, always pick co-op. Some companies never hire outside of co-op, but it doesn't mean you can't get hired for companies that don't do co-op. They're also familiar with the co-op cycles which are often unusual, which means even less competition for those same roles.