This question was asked a long time ago but never got an answer. I get questions like this from my students. Here's what I tell them.
Should I shoot for the moon or focus on other things besides REU for this summer?
As a first-year student, it is very early to be applying to REUs. Most REU slots go to rising seniors, and a handful go to rising juniors. There is no expectation at all that a rising sophomore will do an REU, because after just one year of college, their knowledge base is still insufficient for most research. A better use of that first summer would be to teach yourself something that's not in the curriculum, or do some independent projects (e.g., implementing algorithms you learned) and put the results on Github. It's also perfectly fine to just work a summer job unrelated to your major and make a bit of money, or to travel, or just hang out. Soon enough, there will be an expectation to do things during the summer that go on your CV, so that might be an argument for taking advantage of the fact that in this summer there is no such expectation. I used the summer after my first year to go backpacking in Australia and New Zealand, and that was a wonderful opportunity for personal growth. I did REUs the summers after my sophomore and junior years.
Ok, but suppose a student really has their heart set on a research opportunity. There are some that are tailored for younger students, e.g., at my university in the USA we have an S-STEM grant from the NSF that funds such students for essentially summer learning opportunities that fall short of what most would call "research."
Being a freshman, would REU admissions look at my lack of one recommendation (most require two) as mitigated by my freshman status, or would I be laughed out of the applicant pool?
Unless the REU specifically seeks first-year students, then you are really going to be competing with the older students and your status does not mitigate a lack of preparation. If you apply for a summer opportunity that wants two letters of recommendation then you should give them two letters. Pick two people who know you well as a student. Ideally that would be two professors that have taught you. A first-year student with any real chance of getting into an REU would have taken a pretty heavy course load, so there should be two professors that know you. If not, you could use one professor and one teacher from high school, but this might indeed hurt your chances. It does not hurt to try, but there are plenty of other opportunities for the summer after your first year. Lastly, it's not a winning strategy to worry about being "laughed out of the applicant pool." Better to try and fail than not try at all, if it's important to you.