She doesn't have any 401k through her job. Recently graduated from Anderson University with a Bachelors in Mathematics, but is currently a server/bartender.
I think she wants to put the 3k in a Roth.
You are getting a lot of wrong answers, albeit practical ones and generally from those who are attempting to be well meaning.
Your daughter is a server/bartender. There's nothing wrong with that. But it's not a career with optimum earning power and longevity that will put her in a strong financial position of safety after you pass away.
What happens to our children after we die? Will they be safe? Can they take care of themselves? These are the core questions that matters to parents as they age.
The best thing for someone in her position to do, is to spend the money to expand her potential career network. The best job opportunities are ones not listed in any advertisement or via some recruiter. They are via word of mouth from insiders with legitimate pull or influence. What is your daughter's opportunity circle right now? She works at a bar? A restaurant? Maybe in a larger setting? I'm not trying to pry into her life, what I'm saying is she, like many others, have a finite range within her old friends, her old classmates, her neighbors, her former employers, the kind of people going in and out of her current job, maybe a gym, etc, etc.
She might be better off volunteering a place where big decision makers congregate. She might be better off taking a different job, that might not have much practical range, but it opens up doors, like working at place that does insurance or health care. She might be better off upgrading to a very nice gym or athletic club in the area, where you have a lot of small business owners and management types around.
When you are young, you want people around you to know your name, think well of you, see your potential, and have some time involved in seeing you in a much larger context.
Obviously this calibrates differently as we are in a worldwide pandemic, and depending on the city and location, the rate of violent crime has spiked and gone out of control in some areas. This is different for daughters than for sons. If anyone has a problem with that, then they do, I don't give a single damn, because it's true.
I'm not saying your daughter is stuck in a dead end job, I don't know the full calibration. I am saying it's easy to dry out your practical circle of opportunity very quickly and end up in a rut.
So no, don't "invest" right now in some retirement fund. Use the money to create more opportunity pathways to get more job/career opportunities that will hopefully uplift her earning power. Once she's in a better place at that level, then invest. Is it good to invest when you are young? Yes. In context. But if she can put herself into more opportunity zones, then if she can increase her annual earning power by 10K-15K-20K a year, then what is the force multiplier for her then?
Entry into these alternate access points usually costs money. Maybe it's joining a Soul Cycle class regularly. Maybe it's joining a certain kind of hobby. Maybe it's spending more time in a different part of town.
People want to help those they know and whom they like and where they have seen a full context of that person over some period of time.