Hey Phoenix,
Yes, that's exactly what I mean. A lot of jobs don't do any kind of check on you before they decide to hire you. So I wouldn't bring up that your documents are different until you're sitting with an HR person or hiring manager filling out your new hire paperwork. Once they've hired you, typically all that happens is they make a copy of your driver's license and SS card to file with your tax paperwork, or they put that same information into the e-Verify website. So you'd need to explain to whoever is doing that paperwork with you that your IDs say one thing, but you go by another. The vast majority of entry level jobs like you described will not do any kind of checking beyond this. Fast food, retail, etc.
If it requires a background or credit check, it should say somewhere in the job ad (usually near the bottom, it'll say something like "Hiring is contingent upon successful completion of a background and/or credit check"). You could mention during your interview that you go by a name different than what is on your documents if it is something that you worry about, or if you want to gauge how they feel about trans people. Or you can just wait until they ask you to fill out the paperwork for the background/credit check. Background checks and credit checks can't be initiated without a signature from you, so you could wait until then to say something.
And you could definitely do this with volunteering as well. It may even be easier - a lot of smaller organizations don't require much from volunteers beyond showing up when you say you're going to show up. Some do require some paperwork - hospitals, animal rescues, at-risk shelters, etc. But you can still do the same thing.