what are the chances of someone with a 1300 sat and 3.7gpa who is a urm, first gen, and low income with good ecs, great essay, and great recommendations getting into harvard or similar.
5.4%, more or less. Nobody here can be more accurate than that.
I’m going to go out on a limb here, more so than @skieurope.
With a new SAT score of 1300 (1210–1240 on the old SAT or an ACT equivalent of 27) you have absolutely NO CHANCE at Harvard or any ivy league school, as that score indicates you could not handle the reading, writing and math workload at a competitive school like Harvard, Yale, Princeton etc (sorry),
Don’t believe me? Look at Harvard’s most recent Common Data Set, section C9 SAT and ACT scores: https://oir.harvard.edu/files/huoir/files/harvard_cds_2016-17.pdf. Only 1% to 2% of admitted students had a test score as low as yours, and I can guarantee you that those students had something extraordinary in their files – they were either a recruited athlete in a helmet sport or the son or daughter of a Harvard Alum who donated millions to the school (think Bill Gates’ kids).
However, if were able to increase your SAT score to about 1500, or take the ACT and score a 32-33, that would definitely increase your theoretical chances. Best of luck to you!
Thanks for your response, I would just like to correct you on the old sat conversion. A 1300 on the new sat is equivalent to a 1830 on the old one.
^^ Thank you for that correction. I still stand by what I wrote. Please read this from Harvard’s FAQ golf recruitment page: http://www.gocrimson.com/sports/mgolf/faq
If those are the test scores (2100 based on the old SAT) and GPA needed for a recruited athlete, Admissions is NOT likely to lower their standards for a non-athlete. Best of luck to you!
urm, first generation, low income might mean they would accept slightly lower scores…no one here can tell you though…go ahead and apply to a range of places and include Harvard, but don’t expect anything and you won’t be disappointed 
Make sure you learn about the many great schools out there, including those on the Colleges that Change Lives website. There are many tippy top schools that don’t even require test scores: http://fairtest.org/university/optional though yours are good enough that you might choose not to do that.
An 1830 on the old 3-part SAT is still far, far below the median for Harvard. On the 3-part SAT, the median was around 2200, if not higher.
Fair minus chance. not no chance