Believe it or not, places like Target can be and ARE fairly picky. My sons are constantly applying for part time jobs so I have some thoughts....
1-Look for seasonal work, just to beef up your work experience/ references. THIS is the time. Beginning next month places are going to need tons and tons of extra workers. Apply at every retail establishment known to man. Depending on where you live, there may be other seasonal opportunities such as ski resorts who need hundreds of employees for many various positions for a short period of time. They are not as picky.
2-Kind of tied to #1, look for job fairs. Our local ski resort has a job fair every year and they hire most of that season's staff right there, on the spot.
3-Temp agencies. Use a reputable one. I did this work for many years as a young adult and it ultimately landed me the job that I still have today. You apply through them, so they are the only ones you have to explain your reference situation to, not the companies at which you'll be working.
4-Fast food. It's a drag, but they are MUCH less picky about references and work history. If I recall.... and I could be wrong....McDonalds and/or Burger King don't even ask for references.
These are just ideas for some short term gigs that you can get that will get you something of a work history and also put you in touch with people who can speak to your character/work ethic. If you are friendly and do good work, you could get yourself some nice references. I had a TON of amazing references after doing temp work, for example. After bouncing all over different companies, I had all kinds of people who could vouch for me.
And one other thing. It's true that the vast majority of places ask you to apply online. Do that, of course, but follow up within days of doing so. Call and ASK for an interview. If you think about it, these lower skill jobs can be filled by any trainable body. You get an edge for showing that you are really interested.
Good luck