I have a large, older family and we spend less with three cars and insurance and gas for teenagers.
They can't afford to keep up with the Joneses' when it comes to car choices and transportation. That's the easy place to save some significant monthly expenses. You can get a reasonable car for less than $200/month payment...and insurance and gas for one modest car is substantially less.
Not sure what the $300 monthly miscellaneous expenses are, but a small, young family that operates under a budget and wise spending habits can spend significantly less than $1,350 per month on groceries/eating-out/clothes/diapers/miscellaneous. They should be able to get that well under $1,000. You can also get cheaper phone plans through Mint, Tello, etc.
Can you restructure the $340/month student loans - or get a better job with your degree? Do you qualify for Obamacare subsidy?
Pay your tithing and you can do it!